THE ROYAL COMMISSION ON HISTORICAL MANUSCRIPTS Report on correspondence and papers of HAROLD DAVENPORT (1907-1969) mathematician deposited in the library of Trinity College, Cambridge Reproduced for the Contemporary Scientific Archives Centre No 86/11 THE ROYAL COMMISSION ON HISTORICAL MANUSCRIPTS Quality House, Quality Court, Chancery Lane, London WC2A 1HP 1986 All rights reserved (CSAC 112/3/86) by CSAC 112/3/86 CONTEMPORARY SCIENTIFIC ARCHIVES CENTRE British National Committee for the History of Science, Medicine and Technology under the guidance of the Royal Society’s Catalogue of the papers and correspondence of HAROLD DAVENPORT FRS (1907 - 1969) Compiled by: Jeannine Alton Peter Harper Margaret Erskine All rights reserved Deposited in the Library of Trinity College, Cambridge 1986 H. Davenport GSAG 1 12/3/86 The work of the Contemporary Scientific Archives Centre, and the production of this catalogue, are made possible by the support of the following societies and institutions: The Biochemical Society The Charles Babbage Foundation for the History of Information Processing The Institute of Physics The Institution of Electrical Engineers The Nuffield Foundation The Rhodes Trustees The Royal Society of London The Institution of Mechanical Engineers The Wolfson Foundation H. Davenport CSAC 112/3/86 NOT ALL THE MATERIAL IN THE COLLECTION IS YET AVAILABLE FOR CONSULTATION. ENQUIRIES SHOULD BE ADDRESSED IN THE FIRST INSTANCE TO: THE LIBRARIAN, TRINITY COLLEGE, CAMBRIDGE. H. Davenport CSAC 112/3/86 LIST OF CONTENTS GENERAL INTRODUCTION SECTION A BIOGRAPHICAL AND PERSONAL A.1 - A.137 SECTION B SCHOOL AND UNIVERSITY NOTEBOOKS AND LECTURE NOTES BF 8792 SECTION C LECTURES AND ADDRESSES Cit C2193 SECTION D PUBLICATIONS D1 D213 Introduction to Section D SECTION E RESEARCH NOTES AND DRAFTS E.G. 155 SECTION F Peat tate SECTION G CORRESPO NDENCE G:1:- 6373 BIBLIOGRAPHY Introduction to Section G FACULTY OF MATHEMATICS, CAMBRIDGE INDEX OF CORRESPONDENTS H. Davenport CSAC 112/3/86 GENERAL INTRODUCTION PROVE NANCE The material was received from Mrs. Davenport at various dates 1983 - 84. A little additional material was received from Professor B.J. Birch in 1986. OUTLINE OF THE CAREER OF HAROLD DAVENPORT Davenport was born and educated in Accrington, where his gifts for mathe- matics and chemistry were early recognised. At the age of sixteen he was awarded scholarships to attend Manchester University (1924 - 27) winning first-class honours and the respect of such tutors as L. J. Mordell and E.A. Milne. The latter encouraged him to enter for a scholarship at Trinity College Cambridge, where he read for the Tripos (1927 - 29), began research with J.E. Littlewood, won a Rayleigh Prize (1931) and a Trinity Fellowship (1932 - 37). Another important event of this period was Davenport's acceptance of an invitation by H. Hasse to stay with him in Marburg, a visit which enabled Davenport to meet several distinguished German mathematicians and to first American visit, to Stanford in 1947 - 48, occurred during the London period and University College of North Wales, Bangor. In 1945 Davenport, who had married was followed by many later transatlantic journeys of varying duration. It was also learn the language thoroughly. His first university post was a return to Manchester new journal Mathematika (1953). In 1958 he was elected Rouse Ball Professor of Mathe- Anne Lofthouse in 1944, moved to University College London as Astor Professor. His from the Mathematics Department of University College that Davenport launched the as Assistant Lecturer (1937 - 41) and in 1941 he was appointed to his first Chair at His contributions to his subject, as (which can sometimes only be deduced from a jotted heading on a lecture script) and and work. Less fully represented are his extensive travels for visits and conferences matics and Fellow of Trinity College, Cambridge, where he died in 1969. DESCRIPTION OF THE COLLECTION The collection, which is substantial, covers most aspects of Davenport's life his work for the London Mathematical Society. H. Davenport CSAC 112/3/86 student, teacher, writer and researcher, are however very well documented and the collection as a whole is of pedagogical interest. Section A (Biographical and personal) includes Davenport's own unpublished reminiscences and reflections on his life's work, made shortly before his death with the assistance of his wife and his colleague D.J. Lewis (A.8 -A.10). Other docu- mentation on his career includes, unusually, his examination scripts and marks awarded at Manchester University in 1927, preserved by his principal tutor, L.J. Mordell (A.30, A.3]1). Section B (School and university notebooks and lecture notes) is an interesting record of the state of the art in mathematical teaching at Manchester 1924 - 27 (B.23 - B.54) and Cambridge 1927 - 32 (B.55 - B.92), comprising as it does notes, carefully taken and carefully preserved by Davenport, of lecture courses, class work and exercises. Section C (Lectures and addresses) is a substantial section representing Davenport's own contribution to the teaching of mathematics from the 1930s as a Research Fellow in Cambridge through his various university appointments and invitation lectures abroad, including the lectures at Michigan, later published in book form (C.115 - C.124). Several of these contain sets of problems and solutions, and some examination with permission on pp. 125-130. In addition, there is considerable material relating to work not listed in the made by C.A. Rogers, his research student, collaborator and eventual successor in 1958 as Astor Professor (C.167). School, Davenport's old school (C.131). Conversely, a new generation in the filiation material. Ona less technical note is the address given in 1947 at Accrington Grammar Section D (Publications) includes drafts, sometimes accompanied by correspondence papers. These have been linked wherever possible to the numbered list in the Bibliography of mathematics is represented by the notes on Davenport's lectures at London in 1946 with collaborators (see especially D.110-D.120) or publishers, for Davenport's many appended to the Royal Society Memoir by C.A. Rogers and others (Biographical Memoirs official bibliography; this includes Davenport's books on The higher arithmetic (D.89 - of Fellows of the Royal Society, 17, 1971); a copy of the Bibliography is reproduced D.92) and Multiplicative number theory (D.170 - D.182), book reviews (D.208), unpublished work (D.201 - D.203) and a posthumous publication (D.207). H. Davenport CSAC 112/3/86 Section E (Research notes and drafts) is so titled for convenience only. It contains a variety of material: paginated narrative sequences perhaps intended for lectures or papers, notes and calculations often on problems arising from work by others, and miscellaneous shorter unidentified notes. There is in consequence some potential overlap with other sections, notably Cand D. Off interest is the collaborative work with Helmut Hasse arising from Davenport's period in Marburg (E.1 - E.15). There are also Davenport's notes of lectures and talks by others (E.103 - E.126) which include mathematicians of an older generation (K. Mahler, L.J. Mordell, C.L. Siegel), friends and contemporaries (P. Erdés, H.A. Heilbronn), pupils and successors (B.J. Birch, J.W.S. Cassels, C.A. Rogers, K.F. Roth). Another interesting link in the pedagogic chain is J.E. Littlewood's extended list of 'Research Problems’ and Davenport's 'Comments' (E,131) Section F (Faculty of Mathematics, Cambridge) is relatively scanty but includes a little material on research, examinations and the newly-created Department of Applied Mathematics and Theoretical Physics. Section G. (Correspondence) contains several substantial sequences, though the general practice of longhand correspondence often produces tantalising gaps. Once again, Davenport's links as student, teacher and collaborator with several generations G.278), among many others, indicate his continuing contributions. Special mention must be made of Davenport's close connection with German (G.208) show their recognition and fostering of Davenport's talent, and that with mathematicians, several of whom he met during his early visits to Marburg and elsewhere and whom he helped and encouraged when they were forced to emigrate. Corres- can be traced. Early correspondence with E.A. Milne (G.206) and L.J. Mordell pondence with H.A. Heilbronn (G.123 - G.142), H. Kober (G.165), K. Mahler (G.194 - E. Bombieri (G.28 - G.39), D.J. Lewis (G.175 - G.184) and C.A. Rogers (G.268 - elsewhere in the collection. language is evident both in the corres pondence and in the drafts for lectures and papers G.201), R. Rado (G.257) may be cited as examples. There is also correspondence with H. Hasse (G.116 - G.122) who remained in Germany. Davenport's command of the H. Davenport CSAC 112/3/86 ACKNOWLEDGEMENTS We are especially grateful to Mrs. Anne Davenport for her initial work in assembling the material and making it available, for invaluable provision of notes and information, for her instant recall of names, facts or handwriting, and for her unfailing help and encouragement throughout the compilation of this catalogue. We gratefully acknowledge the help of Professor B. J. Birch in providing information and identifying documents, and in making available his own collaborative correspondence with Davenport as well as material on posthumous publications and the Royal Society Memoir. Oxford 1986 Peter Harper Jeannine Alton Margaret Erskine H. Davenport CSAC 112/3/86 SECTION A BIOGRAPHICAL AND PERSONAL A.1 -A.137 A.1 -A.7 Obituaries and tributes A.8 -A.14 Autobiographical writings A.15 -A.91 Career, honours and awards A.92 -A.129 Diaries A.130-A.132 Miscellaneous items A.133-A.137 Photographs OBITUARIES AND TRIBUTES Obituary from The Times, 10 June 1969; additional tribute by L.J. Mordell, ibid., 19 June 1969. Entry for Who's Who in Europe, sent by publishers for correction; received after Davenport's death. Tributes by L.J. Mordell and by C.A. Rogers (reprints from Acta Arithmetica, 1971). Includes 2pp. plan allocating work between collaborators, corres- pondence, drafts of various sections of Memoir. Correspondence and material relating to Memoir of Davenport by C.A. Rogers, D.A. Burgess, H. Halberstam and B.J. Birch (Biographical Memoirs of Fellows of the Royal Society, 17, 1971). ‘Cambridge between Two Wars'. H. Halberstam's entry for Davenport for Dictionary of National Biography, 1961-70. Reprint of Memoir. Reprint of revised version of above for Bulletin of the London Mathe- matical Society, 4 (1972). : Ip. photocopy giving reference to Davenport from T.E.B. Howarth's H. Davenport CSAC 112/3/86 Biographical and personal Typescript biographical notes made by Mrs. Davenport after her husband's death, in the form of chronological lists, as follows: Visits made by German, and other, mathematicians from 1933 onwards, initially at Davenport's rooms in Trinity College, Cambridge. Visits to conferences, foreign universities and institutions, 1931-68. Students supervised by Davenport at Cambridge, 1959-69. AUTOBIOGRAPHICAL WRITINGS Davenport, although very ill, made notes on his early life and his work, with the assistance of his wife and D.J. Lewis, in 1969; he died in June of that year (see Memoir, p.165). can be found at A.8-A.10. The reminiscences Some, probably earlier, ms. notes onhis career survive, as well as notes on his impressions of America and some humorous writings. 'Reminiscences' Ms. draft of account of his own career in mathematics. reference is 1958. The latest ‘Reminiscences of Harold Davenport, dictated to A.D.' Typescript of Davenport's comments on his own published papers, 1-120 (see Bibliography), dictated to his wife and D.J. Lewis, 1969. Typescript made by Mrs. Davenport of her husband's account of his early life to 1929, with reference to his childhood, family back- ground and his undergraduate days at Manchester. prompted by visit to a conference there, September 1966. Typescript notes re impressions of American institutions, from visit of 1947-48. ‘Come to Russia’, 1966. 2pp. ms., humorously describing the fate of the tourist in Moscow. App. miscellaneous ms. autobiographical notes, n.d. H. Davenport CSAC 112/3/86 Biographical and personal A.14 Ms. notes, made on file-cards, redefining certain concepts, such as ‘inflation’ and 'education', n.d. Davenport's letter to Editor of The Times re ‘inflation’, 1968. Cutting only. Ip. ms. list of non-mathematical quotations, possibly for use in speeches. A.15-A.91 CAREER, HONOURS AND AWARDS SCHOOL CAREER, 1917-24 A.15-A.18 Accrington Grammar School (until 1921, The Municipal Secondary School), termly reports 1917-24. A.15 December 1917-July 1919 A.17 July 1921-December 1922 A.20-A.23 Matriculation Certificate, July 1922. Higher School Certificate, July 1924. A.16 December 1919-April 1921 A.18 March 1923-July 1924 "List of Successful Candidates, School Certificate A.20 Examination, July 1922'. Educational certificates, 1922-24, issued by Joint Matriculation Board. Two letters from Lancashire Education Committee, 1920, re "Open Junior Exhibitions', one of which was awarded to Davenport. (See A.27 for questions papers.) School Certificate, July 1922. A.21 A.22 A.23 H. Davenport CSAC 112/3/86 Biographical and personal Letters from headmaster, 1924, 1927. Letter from old school friend, signed Bottomley, 1934. Invitation to the 'Prize Distribution’, 1947, at which Davenport gave the address (for text see C.131). Also included here is local newspaper with report. THE VICTORIA UNIVERSITY OF MANCHESTER, 1924-27 Letters to Davenport re various scholarships, from the University and Lancashire Education Committee, 1924. A.27-A.29 Examination papers taken by Davenport, 1924-26. A.27 Entrance Scholarships, May 1924. Honours School of Mathematics, Part I, May 1925. ‘Christmas Terminal Examinations', December 1925. A320; AB! Higher School Certificate Examination, July 1924. also A.23. See A 2h. Honours School of Mathematics, Part Il, May 1926. Two examination scripts written by Davenport for the Honours School of Mathematics, Part IIl, May 1927, set, marked and preserved by L.J. Mordell, who sent them to Mrs. Davenport in 1971. See also A.134, A.135. Covering note (A.30), gives names of other examiners, Bailey, Milne and Chapman, which papers they set and Davenport's marks for each. Degree Day programme, July 1927. H. Davenport CSAC 112/3/86 Biographical and personal TRINITY COLLEGE, CAMBRIDGE, 1927-36 Davenport was an Affiliated Student, 1927-29, taking a second 'first' degree, and in 1932 was awarded a research fellowship. Correspondence from Trinity College, 1926-29, re scholarship, status as an Affiliated Student, award of exhibition and the Walker Prize (1929). Letter from the Victoria University of Manchester, July 1927, re scholarship and other arrangements. Trinity College classlists, 1928; ms. note of 'May Marks'; battels bill for Michaelmas Term, 1929. inter-college examination paper, n.d.; 'The continuation of analytic functions', 1928. Ms. of essay submitted by Davenport for Yeats and Rouse Ball Prizes. Dissertation submitted for a fellowship, 1932. Typescript only, in three parts. letters Note from J.J. asking Davenport 'to represent the College’. Thomson, 1936, re weekend visit to 'Christ-Church', Also included are two notes re mathematical problems from J.E. M.A. certificate, Cambridge, 1933. Telegram announcing election to fellowship at Trinity, 1932; and telegrams of congratulation. Three letters of congratulation, 1929 and n.d., on Cambridge successes, including two from former mathematics mistress, A. Heap (see Memoir, p. 159). Littlewood, n.d. (see Memoir, p.160). H. Davenport CSAC 112/3/86 Biographical and personal Application for academic post (possibly assistant lecturership at Manchester), 1936. Ms. and typescripts of testimonials by G.H. Hardy, and typescript testimonial by A.S. Besicovitch. Typescript curriculum vitae and bibliography. UNIVERSITY OF MANCHESTER, 1937-41 ‘On the expiry of his Trinity Fellowship in 1937, Davenport was appointed by Mordell to an Assistant Lecturership in Manchester’ (Memoir, p.161). ‘Conditions of Appointment' for post of assistant lecturer, 1937. A.46-A.49 Fellowship of Royal Society, 1940. A.46 Receipts from Royal Society for fees. Sc.D. certificate, Cambridge, 1938. Announcement of appointment, n.d. (press-cutting only). Letter of application for Chair of Mathematics, University of Durham, 1939, with bibliography. H-N A.47-A.49 Letters of congratulation. A.49 O-T, and first names only A.47 A-G A.48 H. Davenport CSAC 112/3/86 Biographical and personal Recommendation by L.J. Mordell to promote Davenport to Lecturer, n.d., probably 1941. Letter announcing re-appointment as Assistant Lecturer, 1941. Letter of congratulation on award of Adams Prize of University of Cambridge, 1941. See also D.5-D.15. UNIVERSITY COLLEGE OF NORTH WALES, BANGOR, 1941-45 Application for Chair of Mathematics, U.C.N.W., 1941 Ms. and typescripts of testimonials from G.H. Hardy and L.J. Mordell, brief curriculum vitae and covering letter. Folder includes 1941 bibliography found with this application. Correspondence from Principal, U.C.N.W., re appointment, July, September 1941. Four letters of congratulation. ‘Memorandum’ re terms of engagement. Letter of thanks from D.R. Pye, Director of Scientific Research, Ministry of Aircraft Production, 1942, to Davenport and staff at Bangor, re 'the bomb ballistic computations’ . J. Mordell as Fielden Professor of Pure Mathematics. Three letters from Vice-Chancellor, University of Manchester, November 1944-February 1945, re possibility of Davenport's succeeding L H. Davenport CSAC 112/3/86 Biographical and personal Correspondence, chiefly from D.R. Pye and G.B. Jeffery, University College London, December 1944-April 1945, re appointment to Astor Chair of Mathematics. The letters run from the initial approach to Davenport to his formal appointment. post (A.55) in favour of London. Davenport declined the possibility of the Manchester Letters of congratulation on appointment to Astor Chair. Invitation to Davenports to attend farewell dinner given by colleagues at U.C.N.W., June 1945. 2pp. ms. speech, probably given at the dinner, by Davenport. UNIVERSITY COLLEGE, LONDON, 1945-58 Typescript outline of mathematics teaching at University College for 1945-46. Invitation to Davenport's inaugural lecture 'The Geometry of Numbers’, 6 June 1946. See C.164. Letter from Stanford University, 1947, inviting Davenport to go as Visiting Professor for academic year 1947-48 See A.56, A.57 for correspondence re appointment and congratulatory letters. matical Society, 1957. Letter accompanying cheque for Berwick Prize of the London Mathematical Society, 1954. Letter inviting Davenport to accept Presidency of the London Mathe- H. Davenport CSAC 112/3/86 Biographical and personal ROUSE BALL CHAR OF MATHEMATICS, UNIVERSITY OF CAMBRIDGE, 1958-69 See Section F for other material on Cambridge and the Faculty of Mathematics. A.61 Brief correspondence re appointment, December 1957-February 1958. A.62-A. 66 Letters of congratulation : A.62 A-C A.65 P-R A.63 D- J A. 66 S - W and unidentified A. 64 uso 5pp. ms. of speech given by Davenport at 'Presentation' to him, 18 June 1958, at University College, London. A.69 invitation cards. A.70-A.72 Letters of congratulation: THE ROYAL SOCIETY'S SYLVESTER MEDAL, 1967 Menu and seating plan of 1967 Anniversary Dinner. Letters from Royal Society informing Davenport of the award, inviting him to attend Anniversary Meeting to receive medal and to Anniversary Dinner, November 1967; Mayor of London, 1968. Letter inviting Davenports to Midsummer Banquet of Lord A.72 First names and unidentified A.70 A-H A.71 M -T H. Davenport CSAC 112/3/86 A.74, A.75 Honorary D.Se., Nottingham, 1968. Biographical and personal A.74 lunch menu. Correspondence re arrangements, etc., programme, A.75 Press-cuttings. DAVENPORT'S DEATH After a period of illness following the removal of a lung, Davenport died on 9 June 1969. (Memoir, p.165.) Letters of condolence: A.76 A.77 A B A.83 A.84 A.78 A.85 A.88 A.81 A.82 A.86 A.87 A.79 A.80 A.89 Unidentified Material re Memorial Service, Trinity College, and London Mathe- matical Society Memorial Meeting. Some loose items. Scrapbook, containing almost exclusively newspaper cuttings re Davenport's career, 1924-1969. The cuttings include some non- mathematical items, such as reports on Accrington Grammar School prize-giving ceremonies. H. Davenport CSAC 112/3/86 Biographical and personal DIARIES, 1924-69 These are all small pocket diaries, mainly university diaries covering the academic year, used chiefly to record appointments and addresses. A.92 A.93 A.94 A.97 A.98 A.9 1924 1924-25 1925-26 1932-33 1933-34 1934-35 1942 1943 1944 1945 A.95 A.96 1927-28 1928-29 ‘ : 1935-36 1939 1945-46 1946-47 1949 1950 : ; ; : ‘ : ; ; ; 1951 1952 1953 1965-66 1953-54 1959-60 1957358 1958-59 1956-57 1954-55 1955-56 1968-69 1966-67 1964-65 1968-69 1967-68 1960-61 1961-62 1962-63 1963-64 H. Davenport CSAC 112/3/86 Biographical and personal MISCELLANEOUS ITEMS 2pp. typescript note of German and Italian mathematicians, listed according to whether they left or remained in their posts before and during World War II, and their political bias. n.d. The first category, 'German refugee mathematicians', including G. Szegé and H. Heilbronn, gives names, subject speciality, former posts and present whereabouts. Davenport states that all were anti- Nazis. The second category, ‘Mathematicians who stayed in Germany', gives name, pre-war post and extent to which individual was involved in Nazi regime. The third category is 'Collaborators'. The fourth category, 'Italian mathematicians’, from information given by B, Segre (Manchester), gives a list of mathematicians ‘dismissed by the Fascists in 1938' and another of anti-fascist mathematicians. See Memoir, p.161. Letter from Secretary of English Speaking Union, 1958, thanking Davenport for suggesting possible members of a selection committee. Postcards sent by friends and colleagues living or visiting abroad, 1948-69. Letter from Union Mathématique Internationale, 1964, asking Davenport to serve on committee to choose candidates for Fields medals in 1966. Not indexed. H. Davenport CSAC 112/3/86 Biographical and personal A.133-A. 137 PHOTOGRAPHS A.133 Photographs of Davenport, 1911-1968. One print (c.1920) shows Davenport with his sister and 'Marion'. A.134,A.135 Graduation, Victoria University of Manchester, 1927. A.134 Two portrait photographs of Davenport. A.135 graduates. Mounted group photograph, probably of mathematics Miscellaneous group photographs, all including Davenport. Includes oe print of Davenport, P. one of 'Professor Mordell's Seminar’ (1938) and one of Davenport, Besicovitch and Littlewood (1967). Erddés and L.J. Mordell (n.d.), International Congress of Mathematicians, Harvard conference, 1950. Group photograph. H. Davenport CSAC 112/3/86 SECTION B SCHOOL AND UNIVERSITY NOTEBOOKS AND LECTURE NOTES -«8,3-~B:92 6.1. -B.g2 ACCRINGTON GRAMMAR SCHOOL, 1921-24 B.23-B.54 THE VICTORIA UNIVERSITY OF MANCHESTER, 1924-27 Notebooks Lecture and class notes B.55-B.92 TRINITY COLLEGE, CAMBRIDGE, 1927-32 Notebooks Lecture notes 8.1 ee ACCRINGTON GRAMMAR SCHOOL, 1921-24 With one exception (B.22), these notebooks contain Davenport's notes and diagrams on physics, chemistry and mathematics, presumably work for the School Certificate (B.1, B.2) and the Higher School Certificate (B.3-B.17), although several are undated. For Davenport's school reports 1919-1924 see A.15-A.18. ‘Practical Chemistry’, dated September 1922. 'Practical Physics', dated September 1922. 'Chemistry', dated 14 September 1920. 'Physics Notebook', dated 14 September. Only B.22 shows Davenport's non-mathematical interests, containing extracts from various writers and drafts of two speeches, possibly delivered to a school debating society. 'Physics [2]', dated March 1923. ‘Inorganic Chemistry [1 J', dated September 1922. "Inorganic Chemistry £2]', dated February 1923. "Physics C1 J', dated September 1922. H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes '"Physics', n.d., probably 1923. ‘Practical Organic Chemistry', dated April 1923. ‘Physical Chemistry', n.d., perhaps 1922-23. "Light', dated September 1923. ‘Organic Chemistry [1]', dated September 1923. ‘Organic Chemistry [2]', n.d., perhaps 1923-24. 'Physics'; first entry dated 14 September 1923. Untitled notebook containing physics theorems, n.d., perhaps 1923-24. : ‘Mathematical Problems', n.d. Some loose enclosures, one dated March 1924. ‘Extracts from various writers’, n.d. 'Hydrostatics &c.', n.d. ‘Chemistry Notes', n.d. 'Mathematics', n.d. Untitled notebook, n.d., containing mathematical problems. Davenport's Accrington address (inside front cover) replaced by address in Manchester. contributes the more to civilisation’. Two loose enclosures: ms. drafts of speeches 'Should Capital Punish- ment be Abolished?' and re question 'whether Science or Art H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes B.23-B.54 THE VICTORIA UNIVERSITY OF MANCHESTER, 1924-27 B.23-B.30 NOTEBOOKS These hard-back notebooks have been arranged by the covering titles with which Davenport labelled them; only two, B.24 and B.29, can be dated (1924-25 and 1925-26 respectively). | None are indexed and only two are paginated (B.29, B.30). B26 B.24 "Mathematics IVa'. ‘Mathematics IVb‘. Note on inside front cover: 'Ist year BSc Hons. Maths Nofes'. ‘Maths. Va'. ‘Maths. Vb’. ‘Maths. Vb (continued)'. ‘Applied Mathematics B'. ‘Applied Maths. D'. Note on inside front cover: 'Second year BSc. Honours Maths notes’. ‘Applied Maths D (cont'd)'. H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes B.31-B.54 LECTURE AND CLASS NOTES These are loose ms. pages of notes on the literature, notes on lecture courses and class Many bear an indication of the course number, or work and exercises by Davenport. of the person giving the lectures and/or supervising the work. in bulky wallet folders labelled by Davenport; the contents have been removed and where appropriate preserved in more than one folder for ease of reference. The material was kept The original folders are at B.54. See B.85-B.87 for notes originally made at Manchester and subsequently used at Cambridge. B.31, B.32 'Misc. notes & exs. (Lamb &c) 1925-6’. Contents of a folder so inscribed. B.31 dated 1925, 1926. Ms. notes, mainly on Strings, some headed 'Routh', some B.32 Extensive sequence of notes, all headed ‘Lamb’. B.33-B.35 'Exs. 1926-7 and misc.notes 1925-6'. Contents of a folder so inscribed. Contents of a folder so inscribed. Duporcq Chap. VI' and 'Quadrics’. B.33 1926-May 1927. B.34 Transformations. Ms. notes, all headed 'Maths VI b', all dated October Ms. notes, variously titled, including 'Study of Certain Ms. notes, variously titled, including 'Higher Geometry', and B.35 two paginated sequences: 'Real Numbers' (1-5) and ' Infinite Sequences of Real Numbers’ (1-4). May 1927. Ms. notes, all headed ‘Maths Vla', all dated October 1926- B:.. 36, B.37 ‘Summarised notes real var. & exs. Vla 1926-7'. Ms. notes, variously titled, chiefly on integrals and series, B.36 some dated 1927. B.37 H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes B.38, B.39 'Tensor & potential theory 1926-7'. Contents of a folder so inscribed. B.38 Ms. notes on tensors and vectors. Ms. notes, some on ‘sources and doublets’, some on motion. B.39 Includes sequence labelled 'Applied Maths E', dated October 1926- March 1927. B.40-B .43 "Dynamics 1926-7'. Contents of a folder so inscribed. B.40 Ms. notes, chiefly on motion of a rigid body. B.41, B.42 Extensive sequence of notes on various dynamics topics. B.43 October 1926-May 1927. Sequence of notes labelled ‘Applied Maths E', dated Several pages have tutors' comments (#wo hands); work of 31 January 1927 includes separate page of comments. Contents of a folder so inscribed. B.44 Ms. notes, on strain and wave motion. Ms. notes, on potential theory and ellipsoids, with B.46, B.47 "Differential geometry 1926-7'. B.44, B.45 ‘Hydrodynamics & elasticity 1926-7’. several pages marked by tutor, with occasional comment. B.45 sequence of notes labelled 'Applied Maths E', dated October 1926- April 1927; Sequence of notes entitled 'Complex Integration’. Extensive sequence of notes on various aspects of topic, variously sub-titled, including ‘Conditions for a helix' and 'Developable Surfaces’. B.48, B.49 ‘Complex variable notes 1926-7'. B.48 ‘Complex numbers’. B.49 Extensive sequence of notes, variously sub-titled, including Contents of a folder so inscribed. Contents of a folder so inscribed. H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes 250, “6. 35) ‘Real variable notes 1926-7’. Contents of a folder so inscribed. Extensive sequence of notes, headed 'Mathematics VIa', B.50 variously sub-titled, including 'Infinite Series’ and 'Uniform Con- vergence of Infinite Products’. B.51 ‘Fourier Series' and 'Double Integrals’. Three sequences of notes: 'Integrals with parameters’, B:52, B.53 ‘Differential eqns. 1927'. Contents of a folder so inscribed. B.52 "Elliptic Functions’. Two sequences of notes: 'Differ ential Equations’ and Extensive sequence of notes entitled: 'Differential Equations’, B53 variously sub-titled, including 'Properties of Legendre's Polynomials’ and 'Solution of eqns. by definite integrals’. Davenport's original folders from B.31-B.53. H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes B.55-B.92 TRINITY COLLEGE, CAMBRIDGE, 1927-32 B.55-B.64 NOTEBOOKS These hard-back notebooks, excepting B.63, B.64, all contain lecture notes. Davenport usually labelled the fly-leaves with the name of the lecturer, the subject of the course, and the date. These labels are used here, and his descriptions are preserved in the entries. B.63 and B.64 are exceptions as they are without identification, but it is probable that they come from this period in Davenport's career. B.55 'Mr. Pollard Systems of orthogonal functions. Aggregates and functions. 1927-8'. Theory of Integration. S. Pollard was Davenport's Director of Studies for pure mathematics. See Memoir, pp. 159-60. 'Mr. White 1927-8'. 'Mr. Besicovitch sets. Almost periodic functions’. 1927-8. Measurability and the theory of measurable See Memoir, pp.159-60. Prof. Hobson. ‘General Dynamics ‘Mr. Steen. Mr. Pars. Jesus. Michaelmas Term 1928'. ‘Combination of observations. Prof. Eddington Michaelmas Term 1928'. 'Fourier's series and other representations of functions Michaelmas Term 1928'. A.S. Besicovitch was Davenport's Director of Studies for pure mathematics. undergraduate in Cambridge. Two untitled notebooks, n.d., probably from Davenport's period as 18pp. misc. ms. notes enclosed. Classical Theory of Numbers. Lent Term 1928'. ‘Binary forms. Dr. A. Young 1928-29'. H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes B.65-B.92 LECTURE NOTES, ETC. These are loose ms. pages of notes, chiefly of lectures attended by Davenport. Usually they bear the name of the lecturer and the title of the course, and some are dated. The material was kept in wallet folders labelled by Davenport; the contents have been removed and, where appropriate, preserved in more than one folder for ease of reference. The original folders are at B.89. B.80-B.84 are not lecture notes but were probably compiled from textbooks, while B.85- B.87 were probably originally made at Manchester and brought by Davenport to Cambridge for reference. B.65-B.72, B.78-B.84 are dated; the other notes are not, although they are probably of the 1927-29 Cambridge period. B.90-B.92 are lecture, and other, notes from Davenport's post-graduate period, 1929-32. Mr. Contents of a folder so inscribed. B.67 1928'. B.65, B.66 'Mr. Pars. Dynamics’. Contents of a folder so inscribed. B.67-B.70 "Mr. Richmond. Curves & surfaces’. Extensive sequence of ms. notes, variously sub-titled. ‘Algebraic Geometry. Mr. Richmond. Michaelmas Term Extensive sequence of ms. notes headed 'General Dynamics. Pars. Michaelmas Term 1928’. March 1929. B.70 Set of ms. notes (not in Davenport's hand) mostly headed "Kummer's Surface', some also headed 'Richmond', and dates 7-12 Extensive sequence of ms. notes, variously sub-titled. "Curves and surfaces of orders 3 and 4. Mr. Richmond. B.68 Lent Term 1929'. B.69 'Kummer's quartic surface’. 12pp. ms. notes. H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes 'Mr. Hall. Groups’. Contents of a folder so inscribed. 89pp. ms. notes and Ip. 'Summary' headed 'Theory of groups. Mr. P. Hall. King's, Lent Term 1929'. Bz pp.1-45. B7e pp.46-89, with summary. B.73, B.74 ‘Pollard. Volume and surface integrals’. Contents of a folder so inscribed. Extensive sequence of ms. lecture notes, variously sub-titled. B75-S..77 'A.S. Ramsey. Electricity’. Contents of a folder so inscribed. B.75 Miscellaneous ms. notes, some titled. Bi70 30547 Extensive sequence of ms. notes headed 'Solenoids'. B.79 2 February 1928. B.80 ‘Chapter II'. Pencilled note on folder reads: B.78, B.79 Contents of a folder so inscribed. B.80-B .84 ‘Lattice points (Steen)'. Extensive ms. notes headed 'Kinds of definitions' and ‘Ramsey, F.P. Foundations of mathematics’ . 13pp. miscellaneous notes and calculations, 1 page dated Contents of a folder so inscribed. 'Cam. undergrad. 27-29'. B.78 ‘Other views on the Foundations of Mathematics’. Sequence of notes, headed 'Chapter III". Extensive sequence of notes, headed 'Chapter I' and B.84 8pp. ms. notes and calculations. B.81 5pp. ms. notes and calculations. B.82 B.83 Ms. notes and calculations, paginated 22-39. Ms. notes and calculations, paginated 45-77. H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes B.85-B.87 "Series S$ ms Contents of a folder so inscribed. originally made in Manchester as part of Davenport's degree course (see B.25) and later used at Cambridge. These are probably notes B.85 ‘Double Integral over an area’. llpp. ms. notes and calculations, found with cover of Manchester University examination script. B.86 'Va Linear differential equations’. A3pp. sequence of ms. notes and calculations, variously sub-titled. B.87 "Infinite series' Extensive sequence of ms. notes and calculations, variously sub-titled. "A.P. Functions’. Contents of a binder so inscribed. ‘Almost periodic functions’. Sequence of ms. notes and calculations, variously sub-titled. 'A.P. functions of a complex variable’. B.90-B.92 B.90, B.91 B.89 Davenport's original folders from B.65-B.88. Sequence of ms. notes and calculations, variously sub-titled. Two series of lecture notes, found together with note 'Notes of lectures attended at Cambridge’. Lecture notes made by Davenport at Cambridge after taking his B.A. degree. and 'Lebesgue Integral’. Hard -back binder so inscribed, containing typescript lecture notes from a course given by G.H. Hardy, Lent Term 1932. Includes ms. notes and calculations, some titled 'Uniqueness Theory' B.90 "Summable series’. B.91 "Inequalities'. ‘Hardy Fourier series' 1932. H. Davenport CSAC 112/3/86 SECTION C LECTURES AND ADDRESSES C.1 -C.193 C.1 -C.4 CAMBRIDGE, 1930s C.5 -C.12 MANCHESTER, 1937-41 C.13 -C.16 UNIVERSITY COLLEGE OF NORTH WALES, BANGOR, 1941-45 C.17 -C.51 UNIVERSITY COLLEGE, LONDON, 1945-58 C.52 -C.97 CAMBRIDGE, 1958-69 C.98 -C.129 LECTURES ABROAD G3130-Cr1 582 SOCIEMES,. CONFERENCES, etc, C.159-C.193 MISCELLANEOUS AND UNDATED LECTURES G. isC.4 CAMBRIDGE, 1930s Contents of a folder so inscribed, n.d. Extensive paginated ms. draft of a series of lectures on at Trinity College. Oy ay "Algeb. Functions' Cit algebraic functions. C.2 a continuation of C.1. Extensive paginated ms. draft of a series of lectures, probably Not dated, but probably 1933-37 during Davenport's period as research fellow labelled 'Algebra'. Folder includes 3pp. paginated ms. notes and calculations, and label from original folder. "Functions of a complex variable', n.d. Extensive ms. draft of a series of lectures. Extensive ms. draft of a series of lectures, from a folder originally H. Davenport CSAC 112/3/86 Lectures and addresses ©5-C 2 MANCHESTER, 1937-41 The only lecture and teaching material surviving from this period was found in an envelope labelled 'Notes Maths VIII 1940-41'. C5 Duplicated examination paper 'Pure mathematics VIII', December 1940; ms. draft, including solutions to problems set. 9pp. ms. draft headed 'VIII the above. Linear Differential equations' related to Duplicated examination paper 'Pure Mathematics VIII', March 1941; ms. draft, including solutions to problems set. Ip. ms. 'Schemes of Marking' and Ip. ms. 'VIII Homework’. 'D. equations of first order but not first degree’, n.d. 6pp. draft of a lecture. "Notes on exs.' "Solutions in series' "Infinite series'. Ms. draft of course of lectures. ‘Functions of two variables’. Ms. draft of a lecture. Ms. draft, probably for a lecture, giving solutions to various problems and examples. I1pp. miscellaneous ms. drafts, variously titled. Spp. ms .draft, probably of a lecture. "Fourier series’. Ms. draft of a lecture. H. Davenport CSAC 112/3/86 Lectures and addresses C.1B-Gl6 UNIVERSITY COLLEGE OF NORTH WALES, BANGOR, 1941-45 These notes cannot be dated exactly, but all are from the 1941-45 period. All are lecture notes, with no other teaching material. C213 "Fourier series’. Ms. draft of a series of lectures, originally from a folder labelled ‘Bangor’. "Differential equations’. Ms. draft of a series of lectures. "Differential geometry’. Ms. draft of a series of lectures. "Infinite series and integrals’. Ms. draft of a series of lectures. Gi179C. 51 UNIVERSITY COLLEGE, LONDON, 1945-58 This material was probably all intended for teaching undergraduates, and many There are not only finished drafts, both manuscript and typescript, but also notes and lecture drafts are accompanied by reading lists and in some cases by lists of students' names. Ip. ms. list of topics, probably for lectures. Grty Ip. ms. list of topics, probably for a course of lectures, dated 1945-46. calculations. Only C.17-C.34 can be dated exactly. "Ideas for the future’, n.d. H. Davenport CSAC 112/3/86 Lectures and addresses C.18*+C.20 'The natural numbers', 1946. Ms. draft of a course of lectures, some pages dated January 1946. C.18 9 topics, variously titled. 19 4 topics, variously titled. C.20 term' lecture course. 6 topics, variously titled, with Ip. ms. notes for ‘Summer ‘First Year Special Analysis’. 6pp. ms. draft of an introductory lecture to first year undergraduates, found with C.18-C.20. Gute, Mere 'The geometry of numbers', 21948 CZ Ms. draft for a course of lectures. ogo Rough notes and calculations. 2pp. ms. notes and calculations. "Theory of Numbers’. Ip. ms. list of students' names and addresses. '3rd yr Theory of Numbers. 1952"58. Supplementary to "Higher Arithmetic’, Cea, 26 ‘Classical achievements in pure mathematics', ?1952. ‘Quadratic forms (supplementary to "Higher Arithmetic")'. 2pp. ms. outline of a lecture course, giving dates of lectures, with 2pp. ms. notes and calculations. Bangor Mathematical Society, 4 December 1952. Folder also includes 'The fundamental theorem of algebra', given to the Ip. ms. list of the lectures; introductory remarks and lectures Extensive typescript and ms. draft of course of 5 lectures. ©.25 L=3, C26 Lectures 4 and 5. H. Davenport CSAC 112/3/86 Lectures and addresses Case 2? 'Various topics in the theory of numbers', 1953-54. 94pp. paginated typescript draft of a course of lectures. .27 pp.1-41 G.28 pp.42-79 C729 pp. 80-94, and Spp. diagrams. "Remarks to S 1 class', 1955. 5pp. ms. notes of introductory talk to undergraduate class. C Sims "Introduction to the analytic theory of numbers', 1956-57. C.31, C.32 Ms. draft, paginated [1 J-66, of a course of lectures. 2 folders. 33 Ms. draft, paginated 83-133. C34 lecture course; 5pp. ms. notes. 2pp. lists of signatures, probably of those attending the C.36, C.37 2 folders. 'Theory of numbers (Third year course)', n.d. C.36-C,40 'The geometry of numbers', n.d. Contents of a folder inscribed 'G of N (UCL)’. Duplicated typescript with a few ms. corrections. App. ms. draft, probably of first lecture of a course. Ip. ms. note of 'Further topics’. C.40 2pp. list of topics headed 'Geometry of numbers’. C.38, C.39 Another copy. H. Davenport CSAC 112/3/86 C.41-C.51 Lectures and addresses Miscellaneous notes and drafts for lectures, originally kept in an unlabelled binder. order but has been divided into folders for ease of reference. The numbers in the headings of e.g. C.46, C.47, C.48 probably refer to lectures from extended courses. The material has been preserved in its original C.4l paginated 9-12, concerning work by Dirichlet. Miscellaneous ms. notes and calculations, including sequence C.42 "Indefinite forms'. Ms. draft for lecture. C.43 ‘Elem. Theory of Numbers’. 32pp. ms. draft for lecture series; with Ip. ms. reading list. Folder includes 3pp. miscellaneous ms. notes and calculations. C.44 ‘Continued fractions’. 6pp. ms. draft of a lecture, with Ip. ms. reading list. C.45 'Number theory. Outline course’. 2pp. ms. list of lecture titles. Ip. ms. reading list. C.46 '5. Gauss's Sum’. "Higher power residues' . ‘Examples on number theory’. 6pp. ms. problems and solutions. ‘Theory of numbers. Literature’. App. ms. draft, probably unfinished, of a lecture. 8pp. ms. draft of a lecture, probably one of a series. 2pp. ms. draft. C.47 ~—s' II Quadratic residues’. Divisibility and the primes’, 'II] Congruences', 'IV Ip. ms. notes outlining a course of lectures. '5 (k/P) as a function of P'. 3pp. ms. outlines of lectures. H. Davenport CSAC 112/3/86 Lectures and addresses C.48 '2. Gauss's lemma'. 2pp. ms. draft. The law of quadratic reciprocity’. . ms. draft. An algorithm for oe . ms. draft. C.49 Miscellaneous ms. notes, drafts and calculations, all untitled. C.50 for lecture. Miscellaneous ms. notes, including pp.33-39 only of draft C251] Inside cover of original binder, with ms. calculations. H. Davenport CSAC 112/3/86 Lectures and addresses C S297 CAMBRIDGE, 1958-69 All the material here was used for teaching, probably of both undergraduates and postgraduates. Several lectures include lists of problems to be attempted by the students (see especially C.62, C.97); it was Davenport's custom to hand these out at the begin- ning of a lecture course. Some lecture material also includes outlines of the topics to be covered, ms. notes and calculations, and drafts of earlier work, used in the production of the lecture. Ce2-C 54 "Analysis Il. Cambridge lectures’. Contents of a folder so inscribed. C.52, C.53 . ‘Analysis Il 1959-60'. 69pp. ms. draft of a lecture course, with Ip. and topics to be covered. colleague for loan of notes. (C.52). 2 folders. Includes letter of thanks, 1960, from list of dates of lectures C54 ‘The Garnma Function'. Gca5-C. 5? G. 58 Shorter notes and calculations. 3 folders. Miscellaneous shorter notes and drafts. 78pp. ms. draft of course of lectures. 'Diophantine Approximation', 1961-62. C.55 includes list of students’ names and 10pp. draft, possibly of an optional lecture for the end of Cs the course, on Cassels's theorem. C.55-C.57 App. outlines of topics to be covered, Ip. 3pp. preliminary draft and notes. Includes original folder, inscribed with calculations. "Functions of a complex variable (Easter term, 1962)'. C.60, C.61 46pp. ms. draft for course of lectures. 2 folders. Folder includes reprint of Bibliog. 111. C.62 "Problems'; 'Solutions'. H. Davenport CSAC 112/3/86 Lectures and addresses C.83-C. 66 'Theory of numbers (Introductory Part IIl)', ?1963. C.63-C.65 C.65 includes Ip. ms. reading list. 83pp. ms. draft for lecture series, 3 folders. Ip. dated 1963. C.66 Ilpp. ms. draft; miscellaneous ms. notes and calculations. "Two problems of Mordell', 1964. 10pp. ms. draft of a seminar paper, given 25 February 1964. 'The geometry of numbers (Lent Term, 1964)'. C .60e0.70 103pp. ms. draft for lecture course. 3 folders. Coe C.22 Miscellaneous shorter notes and drafts on topics to be covered. 9pp. ms. notes and calculations. Also included here are Ip. ms. notes in an unidentified hand and reprints by K. Mahler. G.73-6..75 Css Miscellaneous ms. notes and calculations. C.73 includes 2 folders. C.76 6pp. ms. draft for lecture. "Theory of numbers (Part Il, Optional)', 1964-65. ‘Diophantine approximation (Michaelmas term, 1964-5)’. C.73, C.74 Ip. list of pupils, October-December 1964. 7l|pp. ms. draft for lecture course. Ip. typescript outline of lecture course, dated October 1964, with Ip. ms. list of topics to be covered in each lecture. Solutions’. 2pp. typescript entitled 'Theory of numbers (Part II), 1964-65 Problems’. 2pp. typescript entitled 'Theory of numbers (Part II), 1964-5 Outline C2 Spp. ms. of questions, problems and examples. H. Davenport CSAC 112/3/86 Lectures and addresses 'The basic inequality of the large sieve method', 1 November 1966. 10pp. ms. draft for seminar paper. 'Dirichlet's L-functions. 2lpp. draft for lecture, with Ip. ms. calculations. (Michaelmas term 1966-7)’. £00-C..85 ‘Additive number theory', ?1967-68. C-80-©., 82 119pp. ms. draft for lecture course. 3 folders. C.B3 sequence re paper by B.J. Birch. Miscellaneous ms. notes and calculations, including 4pp. paginated C.84 'Waring's problem’. Ms. draft, probably for lecture, paginated 4-23. 'Mordell's finite basis theorem’. Cx85 6pp. ms. draft for lecture, with 3pp. ms. notes and calculations. C.86-C.88 'Waring's problem’. The Higher Arithmetic Includes 5pp. alternative version. C.87 'The Hardy-Littlewood method’. C.88 'The Asymptotic formula: Vinogradov’ . 'Cambridge Lectures (additive)', n.d. 60pp. ms. draft for course of 3 lectures from folder labelled as above. C.86 The first page of this lecture was used as the cover illustration of the (1982), although 5th edition of Davenport's the text does not appear elsewhere in the book. 3 folders. CBr. F1 'The distribution of the primes', n.d. 95pp. ms. draft for course of lectures. H. Davenport CSAC 112/3/86 C3295 "The Riemann Zeta-function', n.d. Lectures and addresses C92 "last term's course on the distribution of primes’ (C.89-C.91). llpp. ms. draft for lecture, probably a continuation of C.93, C.94 69pp. ms. draft for lecture course. 2 folders. C.95 Miscellaneous ms. notes and calculations. "References for equations in many variables’, n.d. 3pp. ms. list, possibly to accompany a course of lectures. "Davenport: Theory of Numbers', n.d. Two typescript drafts, 3pp. and 2pp., of list of problems. ‘Davenport: Geometry of Numbers', n.d. Two typescript drafts, 3pp. and 2pp., of list of problems. C.98-C : 129 LECTURES ABROAD up toa full academic year, and could involve teaching and examining as well as lecturing. Stanford, G&ttingen and Michigan. Visits to these institutions were for varying periods Davenport made many visits abroad (see Mrs. Davenport's biographical notes at A.7). The material here is from three universities with which he had particularly close connections: University of Michigan C298. «C107 Stanford University, California C.108-C.114 G&ttingen CittS-C 3129 H. Davenport CSAC 112/3/86 Lectures and addresses C.98-C.107 Stanford University, California, 1947-48, 1950. Davenport was invited by Gabor Szeg4 (see A.60) to spend the year 1947-48 at Stanford as a visiting professor, and he returned there in 1950 (see also Memoir, p.162). C.96-C i102 "Group theory (Stanford)', 1948. Lecture and teaching material, from an envelope so inscribed. C.98 27pp. ms. draft for course of lectures, variously sub-titled. C.99 with Ip. ms. calculations. 13pp. ms. draft for course of lectures, variously sub-titled, C.100 "Abelian groups’. 2 ms. drafts for lecture, 8pp. and 5pp. C.101 "Sylow's Theorem', Ypp. ms. draft. 'Theory of groups', 5pp. ms. draft. C.102 of Course'; Ip. ms. 'Groups Literature’; Ip. ms. 'Group Theory. Outline 3pp. ms. 'Examples on groups’; etc. 67pp. typescript notes made by G. Hedrick. C.105-C.107 ='Draft T. of nos Stanford', n.d. 'Selected Topics in the Geometry of Numbers', Summer Quarter, 1950. Programme of meeting of American Mathematical Society, April 1948, mentioring lecture by Davenport. 22pp. ms. draft for lecture. Ms. draft for course of lectures, with note on first page ‘Analytic number theory ctd.'. Ms. draft of a course of lectures, variously sub-titled. C. 107 "The Hardy-Littlewood method’. C.106 ‘Additive number-theory'. Contents of an envelope so inscribed. Cte "Analytic Theory of Numbers’. H. Davenport CSAC 112/3/86 Lectures and addresses C.108-C.114 Géttingen, 1954 and 1966. In 1966, Davenport was Gauss Professor der Mathematik an der Akademie der Wissenschaften zu Guttingen (see Memoir, p.164), visiting G&ttingen from May to August (see Mrs. Davenport's biographical notesat A.7). He had lectured there previously in February 1954. Virtually all the material here is in German. Davenport had a good command of the language, and had made many German friends and colleagues, particularly among the refugees arriving in Cambridge in the 1930s (see Memoir, p.161). See also G.299-G. 303 for material relating to Davenport's appointment and visit to Géttingen in 1966. C.108 Correspondence with C.L. Siegel, December 1953-January 1954, re invitation to give a talk to the 'Mathematische Gesellschaft’. Davenport chose as his subject 'Simultaneous Diophantine Approximation’. 10pp. ms. draft for lecture, dated February 1954, in German, in several hands. C.109-C.213 33pp. ms. draft. All are in German. C.109 C79 Corr 32pp. ms. draft; Ip. ms. notes. "Schlecht approximierbare Zahlen'. 'Ausgewahlte Fragen der Zahlentheorie' . 'Die Verteilung der quadratischen Reste und Nichreste’. Lectures delivered May-August 1966, originally found together in an envelope labelled 'Lectures G&ttingen'. in English) . 19pp. ms. draft; 9pp. miscellaneous ms. notes and calculations (2pp. Cero 'Gleichungen und Identitdten'. 20pp. ms. draft. Colt? ‘Uber y2 - x3! 9pp. ms. draft, paginated 38-46. H. Davenport CSAC 112/3/86 Lectures and addresses Topics for G&dttingen'. Ip. ms. list of topics, probably for lectures given in 1966. C.115-C.129 University of Michigan, 1962-68 Davenport had a fruitful association with Michigan, where he was a frequent visitor in the 1960s. His principal collaborator was D.J. Lewis; Davenport's lectures at Michigan in 1962 on 'Analytic methods for Diophantine equations and Diophantine inequalities' were published in 1963 (see C.115, G.175-G.184, and Memoir, p.167). C.118 ‘Analytic methods for Diophantine equations and Diophantine inequalities’, 1963. Bound photocopy of a course of lectures given at Michigan in the Fall Semester, 1962. Contents of a folder so inscribed. cto 'Goldbach's Problem’. lépp. ms. draft. C.116 1962. 26pp. ms. draft. C.116-C.124 ‘Michigan Lectures’. "Analytic methods for Diophantine equations and inequalities’, Folder includes letter from publishers, 30 July 1963, outlining publication agreement. Original folder inscribed with calculations. C .449 lépp. ms. draft. C.119-C.121 Variously titled and paginated shorter ms. drafts. 3 folders. 'Vinogradov's result on sums of 3 primes’. Go ee Untitled ms. draft paginated 24-40A. Crile Questions papers, etc. C.124 H. Davenport CSAC 112/3/86 Lectures and addresses "Modular fns' 'Notes of seminar Mich. 1965?' Extensive ms. notes and calculations, originally found in inscribed. a folder so C,126-G-129 Series of 4 lectures, given 3-7 September 1968. C126 ‘Diophantine approximation: an introductory survey’. 15pp. duplicated typescript with ms. corrections. C127 ‘Badly approximable numbers’. Ilpp. duplicated typescript with ms. corrections. Gal2s "Dirichlet's theorem’. 17pp. duplicated typescript with ms. corrections. Crag ‘A problem of Diophantus'. l5pp. photocopy of ms. draft. C.130-C.158 SOCIETIES, CONFERENCES, ETC. of Davenport's many visits and conferences. C.152-C.156 contain material which cannot be accurately dated, and C.157, C.158 societies, including undergraduate clubs. It does not however present a complete record consist: of invitations and programmes. Of particular interest is C.131, Davenport's address The material here consists mainly of drafts for lectures given at conferences and to See also A.25. 19pp. duplicated typescript draft (in French); two programmes of lectures, April-May 1946, of Institut des Hautes Etudes de Belgique. Address given at Accrington Grammar School prize day, 26 March 1947. 8pp. ms. draft and Ip. notes; re arrangements; programme. letter from headmaster, 20 March 1947, given at the prize day of his old school. C130 "La géometrie des nombres', Brussels, 1946. H. Davenport CSAC 112/3/86 Lectures and addresses ‘Some American Impressions', Presidential address to the Mathematical and Physical Society, University College, London, 29 October 1948. ll pp. typescript draft. 6.193, C. 184 'G.H. Hardy', 1948 and n.d. Case App. untitled ms. draft of a lecture, delivered in 1948. 7pp. ms. draft and notes for a talk to an unnamed society re Hardy's Collected Papers, n.d. Davenport was on the London Mathematical Society committee set up to edit Hardy's papers, and did much work for it (see Memoir, p.165) llpp. ms. draft and notes, partially paginated, for a talk toan un- named undergraduate society re Hardy's career and publications, n.d. C.134 with Ip. ms. notes by Davenport. Reprint of E.C. Titchmarsh's L.M.S. memoir of G.H. Hardy, 3pp. photocopy of Hardy's 1914 paper on Riemann functions. 'A great Oxford mathematician’ (H.J.S. Smith), Invariant Society, Oxford, 3 May 1950. Ilpp. typescript draft with ms. corrections. C.136, C.137 'Diophantine Approximation’, 1952, 1954. 7pp. ms. draft of version delivered to Oxford Mathematical l4pp. ms. draft of version delivered to British Mathematical C.136 Colloquium, Greenwich, July 1952. Alpp. typescript draft for lecture (in French). Rough outline of 'informal' talk at Queen Mary College, London, 4 February 1954. 'Problémes d'empilement et de recouvrement', Rome 1955. ctor Society, 3 March 1954. 4pp. ms. draft and notes re Diophantine approximation. App. ms. draft re lattice points. 2pp. ms. only. H. Davenport CSAC 112/3/86 Lectures and addresses "Indefinite quadratic forms in many variables', St. Andrews, September 1956. App. ms. draft for lecture or talk. "Some recent work'. Lecture to the theory of numbers group at the British Mathematical Colloquium, Nottingham, 11 September 1957. 7pp. typescript draft and 4pp. miscellaneous ms. notes and calculations found with it. "Analytical number theory’, ?1958. App. ms. notes also headed ‘Edinburgh 4 hour', for short talk at International Congress of Mathematics, August 1958. See also D.121. "The nature of mathematics', 1958. 8pp. ms. draft for talk given to the Trinity Mathematical Society, 20 November 1958. 6pp. ms. draft; ms. notes and calculations. London, 5 March 1959. See also C.160. Spp. ms. notes. "Equations in integers', New Pythagoreans, 21 January 1959. Speech given at dinner of Mathematical and Physical Society, University College "Les Equations diophantiennes 4 plusieurs variables' and 'Les inégalités diophantiennes a plusieurs variables', lectures delivered at the Faculté des Sciences, Université de Paris, in 1860. App. and 8pp. ms. drafts for talk given in the centenary year of Dirichlet's death; Ip. ms. notes made by Davenport from talk given by Kummer Duplicated typescript drafts; 1959. 6 and 7 April 1959. letter of thanks from P, Dubreil, 20 July "Dirichlet', 1959. H. Davenport CSAC 112/3/86 Lectures and addresses 'Diophantine approximation', lecture delivered at the British Mathe- matical Colloquium, Southampton, 13 April 1962. 15pp. ms. draft. Copy of report by Davenport on a visit to Poland, 18-30 March 1963, under arrangements for exchange visits of scientists between Polish Academy of Sciences and Royal Society. . Davenport gave 3 lectures during his visit and worked with A. Schinzel. Conference at Oberwolfach, 1-5 April 1963 (after Polish visit). 8pp. duplicated 'Tagungsbericht'. lecture on Diophantine equations in many variables’. See p.4 for abstract of Davenport's ‘Irrational numbers', lecture to the Tensor Club, 6 February 1964. l4pp. ms. draft and calculations. ‘Report on visit to the University of Vienna', 6-19 April 1964. Ip. ms. draft. Bound copy of lecture; 2 ms. drafts, 6pp. and l4pp., with first page only of an early draft, all in German. "Diophantische Gleichungen in mehreren Unbekannten', 15 April 1964, given during visit to Vienna. ‘Quelques découvertes récentes dans la théorie des nombres', lecture given at the Université de Grenoble, 16 June 1967. 3pp. ms. notes entitled 'Brighton', found with it. H. Davenport CSAC 112/3/86 Lectures and addresses G152-C. 156 Undated lectures for societies or conferences. Gi152 "Packing and covering by spheres’. 2 ms. drafts, both 7pp., of a talk, one labelled 'copies Harvard lecture’. "Problems of packing and covering’. 9pp. typescript draft, perhaps a later version related to Bibliog. 160. C153 "Simultaneous Diophantine approximation’. 2 ms. drafts, both 4pp. 5pp. typescript draft, with ms. corrections, of ‘Congress lecture’. C.154 "Kongruenzen vom additiven Typ’. 12pp. ms. draft. C.155 'The large sieve inequality’. : 12pp. ms. draft of 'Lecture delivered somewhere’. C.156 'Un probléme d'approximation Diophantienne’. 12pp. ms. draft. C.157, C.158 Invitations and programmes. Announcements of 2 London Mathematical Society lectures Letter inviting Davenport to session of International Congress i. 158 of Mathematicians, 18 June 1949. C3167 delivered by Davenport, 1946 and 1968. Programme of conference at Rome, 1968. Programme of the Mathematical Association, 1949-50. Programme of conference at Brussels, 1955. H. Davenport CSAC 112/3/86 Lectures and addresses C.159-C.193 MISCELLANEOUS AND UNDATED LECTURES Included here are two collections of lecture material (C.159-C.170 and C.182- C.193) which have been kept together in the order in which they were found. The first of these collections is chiefly material concerning the geometry of numbers, while the second is far more miscellaneous in character, being mostly notes and calculations. C.171-C.181 consists of miscellaneous lectures which cannot be dated, although most have titles. C.159-C.170 'GofN lectures’. This collection of lecture notes was found together in a folder inscribed as above. Most deal with the geometry of numbers and some are dated (1946-59). They have been kept in their original order. Of particular interest is C.167, C.A. Rogers's notes of a course of lectures given by Davenport, and an account of the seminar and dis- cussion of the lectures. ce 159 "Marshall Hall's Theorem on Continued Fractions', n.d. 12pp. ms. draft, probably of a lecture, with Ip. ms. diagram. l6épp. ms. notes. See also C.144. C.162 Mathematical and Physical Society dinner, UCL, 9 March 1956. 'General Functions', delivered to the Mathematical and Physical C.161 (a Cambridge undergraduate society), 23 November 1949. "Some doubts about mathematics', delivered to the 'Archimedeans', C.160 Society, University College London, 5 March 1959. 2pp. typescript. C.164 Professor of Mathematics, University College, London, 1945. C.165 to the A.M.A., Berkeley, 24 January 1948. ‘Abstract of Lecture on the Geometry of Numbers', delivered 163 "Progress in number-theory since 1930', n.d. 9pp. ms. draft of and notes for a talk. "Inaugural lecture’, probably given on appointment as Astor l0pp. typescript draft with ms. corrections. 7pp. ms. draft for speech. Various ms. and typescript drafts. H. Davenport CSAC 112/3/86 Lectures and addresses C.166 1 April 1948. "A theorem of Minkowski', lecture delivered at Berkeley, 8pp. ms. draft. C.167 "The Geometry of Numbers’. Ms. notes made by C.A. Rogers from Davenport's lectures at University College, London, 1946, with 'an informal account of the meetings of a seminar held at University College, and includes a summary of the dis- cussion of the various lectures’. C.168 delivered at Cambridge seminar, 8 February 1946. 'Non-homogeneous problems in the Geometry of Numbers', Spp. ms. draft. C.169 "La géométrie des nombres', n.d. 18pp. typescript draft for lecture, with ms. corrections (in French). C.170 'The Geometry of Numbers', n.d. 22pp. ms. draft for lecture, an English version (probably earlier) of C.169. Includes label from original folder. Note on first page 'P.G. lectures ?U.S.' "Abundant numbers', n.d. 12pp. ms. draft for lecture. 57pp. typescript draft, with ms. corrections, for course of lectures, n.d. Ip. ms. 7pp. typescript draft, with ms. corrections, of a lecture; "Some unsolved problems’. 12pp. ms. draft of a talk. "Solved and unsolved problems of mathematics’. 2 ms. drafts, 6pp. and Spp., of a talk. ‘Solved and unsolved problems’. H. Davenport CSAC 112/3/86 Lectures and addresses C.174 *Some curious series’. 17pp. ms. draft of and notes and calculations for a talk. "Diophantine equations in many variables’. 19pp. ms. draft for lecture. ' Jarnik and Walfisz’. 10pp. ms. draft for lecture; 3pp. ms. calculations. 177 C A7S "Diophantine approximation’. C.177 Ip. ms. outline of course of 5 lectures. 2|pp. incomplete ms. draft of a series of lectures, paginated 1-13, 95-100. i i7e 2lpp. miscellaneous ms. notes and calculations. "Geometry of Numbers’. llpp. ms. notes for 3 lectures. "Plans for G. of N. course’. 9pp. ms. notes and calculations. 3pp. untitled ms. draft of an after-dinner speech re nature of mathematical Ypp. untitled ms. draft of a lecture re 'some of the most important applications of analysis to the theory of numbers’. Included here isa Ip. ms. list of topics, probably for a lecture course, headed 'Hilbert'. progress. H. Davenport CSAC 112/3/86 C.182-C.193 "Misc. math.' Lectures and addresses Contents of a folder so inscribed, described by Professor B. J. Birch (February 1986) as: 'a mixed bag of lecture notes for various courses given mainly at University College. published in "Multiplicative Number Theory"' (see D.170-D.182). Some of the material was eventually The material has been kept together in the order in which it was found. C.182 2pp. miscellaneous ms. notes and calculations. 6pp. ms. notes and calculations headed '5. of forms’. The coefficients in a period C.183 App. ms. draft headed 'The reduction of a pair of linear forms'. 2pp. ms. notes and calculations. Reprint of Bibliog. 75. C.184 squares’ , 5pp. ms. draft headed ‘Representation of numbers as sums of 2pp. miscellaneous ms. calculations. 185 5pp. paginated sequence of ms. notes and calculations. 187 'Zeta-function and L-functions'. 19pp. ms. draft. C.186 6pp. miscellaneous ms. draft and calculations. 3pp. sequence of ms. notes and calculations. 6pp. miscellaneous ms. notes and calculations. 5pp. miscellaneous ms. notes and calculations. 3pp. ms. draft headed 'Chapter 6. Characters’. function’. Spp. ms. draft and notes headed ‘Alternative treatment of the Zeta- Spp. ms. draft and notes headed 'The Riemann-Zeta function’. C7189 Spp. sequence of ms. notes. C.188 'Cyclotomy'. 13pp. ms. draft and calculations. H. Davenport CSAC 112/3/86 Lectures and addresses C.190 6pp. miscellaneous ms. notes and calculations. 2pp. ms. draft headed 'The prime-number theorem’. Ip. ms. calculations. Spp. sequence of notes. Ale ‘Geometry of numbers’. 15pp. ms. draft. C.192 "Algebraic numbers’. 17pp. ms. draft. C.193 headed 'Chapter VI. A method of Carlitz’. Miscellaneous shorter notes, drafts, tables, etc., one draft H. Davenport CSAC 112/3/86 SECTION D PUBLICATIONS D.1 - D.213 Davenport published nearly 200 papers, as well as three books. Most of the material in this Section consists of drafts of the published papers, frequently without any other material such as notes or calculations. In some cases however these do survive and in others there is more than one draft. Some correspondence is included here, for example, D.112 -D.116. The sequence incorporates material of other kinds, such as the Adams Prize Essay (D.5 - D.15), the books The higher arithmetic (D.89 - D 92) and Multiplicatative number theory (D.170 - D.182), reviews by Davenport (D.208), and some unpublished material, such as 'On writing mathematical papers' (D.201 - D.203). Material published after Davenport's death can be found at D.204 - D.207, and his ‘collected works' are represented at D.210 - D.213. The material has been arranged in chronological order, and where applicable the Bibliography number of the Royal Society Memoir has been given, as well as the date of publication. D.1 'On certain exponential sums', 1933 (Bibliog. 5). 3lpp. typescript draft with ms. corrections; Ip. ms. calculations. tions, see the relevant entries in Section G and also E 1 - E 15 (work with H. Hasse). 'On the product of three linear homogeneous forms (II)', 1938 (Bibliog.25). For additional correspondence and material exchanged with collaborators in publica- 19pp. typescript draft (incomplete), with ms. corrections; 4pp. type- script draft. 30pp. ms. draft. 'On the product of three homogeneous linear forms (III)', 1939 (Bibliog. 26) "On Waring's problem for fourth powers', 1939 (Bibliog. 35). 37pp. typescript draft with ms. corrections. H. Davenport CSAC 112/3/86 Publications Adams Prize Essay for 1939-40. The essay contains material published in various papers, 1938-46 (including D.2-D.4). The material here includes early drafts of certain chapters (D.5, D.6), the whole text, probably as submitted to the judges (D.8-D. 14) and a little correspondence. D.5, D.6 together in an unlabelled folder. Early ms. drafts of various chapters of the essay, found 0.5 jecture of Mordell'. 2ms. drafts, 3pp. and 5pp., for ‘Chapter VI On a con- 9pp. ms. draft and calculations for 'Chapter VII Minkowski's conjecture and Remak's theorem'. D.6 9pp. ms. draft headed 'W.P.'. 2pp. ms. draft for ‘Chapter VI On sums of pos. & neg. 4th powers’. D.7 31 December 1940. Ip. ms. 'Contents of Essay'; 3pp. typescript abstract dated As the D.8-D.11 ‘Part One. D.12-D.14 'Part Two. On Waring's problem’. Introduction, Chapters I-VII, in 3 folders. Introduction, Chapters I-VII, in 4 folders. On the Geometry of Numbers’. D.15 Includes letter of 29? May 1941 informing Davenport of award. Brief correspondence re Adams Prize Essay, 1941, 1942. D.8-D.14_ Ms., typescript and printed text of the essay. material for many chapters had already been published, much of the essay was presented in the form of pages from the printed texts pasted onto file paper. Originally found in two ring-binders, the material has been divided into folders for ease of reference. 6épp. ms. draft. ‘On sums of positive integral kth powers', with P. Erdés, 1939 (Bibliog. 36). 'On linear fractional substitutions with large determinant', 1940 (Bibliog. 32). App. ms. draft (Erdds's hand). H. Davenport CSAC 112/3/86 Publications "Note on the product of three homogeneous linear forms', 1941 (Bibliog. 39). App. ms. draft. 'On a conjecture of Mordell concerning binary cubic forms', (Bibliog. 40). 1941 12pp. typescript and ms. draft. D.20-D.22 'On sums of positive integral kth powers', 1942 (Bibliog. 34). D.20 D.21 D.22 App. ms. notes. 18pp. ms. draft. 6pp. galley-proof, with ms. corrections. "On Waring's problem for fifth and sixth powers', 1942 (Bibliog. 37). l4pp. ms. draft. 4 ms. drafts, 6pp., 7pp., l0pp. and IIpp. D.24, D.25 9.26, 0.27 D.24 D.25 D.26 D.27 Ip. ms. calculations, 14pp. typescript draft. "Qn the minimum of a binary cubic form', 1943 (Bibliog. 41). "On the product of three homogeneous linear forms (IV)', 1943 (Bibliog. 42). 10pp. ms. draft. ‘On the minimum of a ternary cubic form', 1944 (Bibliog. 43). Ms. draft paginated 1-45 (p.24 missing). 32pp. ms. draft. H. Davenport CSAC 112/3/86 Publications 'The reduction of a binary cubic form (I)', 1945 (Bibliog. 45). 8pp. typescript draft with ms. corrections. 'The reduction of a binary cubic form (II)', 1945 (Bibliog. 46). 12pp. ms. draft; 8pp. typescript draft with ms. corrections. 'On the minimum of x? +y? +z3"', 1946 (Bibliog. 44). 2 ms. drafts, 5pp. and 6pp. ‘Simultaneous Diophantine approximation', with K. Mahler, 1946 (Bibliog. 47). 8pp. ms. draft; 6pp. typescript draft. 'On a theorem of Tschebotareff', 1946 (Bibliog. 48). 2 ms. drafts, each 7pp. 8pp. ms. draft. "Non -homogeneous binary quadratic forms', 1946 (Bibliog. 51). 12pp. ms. draft (Heilbronn's hand); 9pp. ms. draft. 'The product of n homogeneous linear forms', 1946 (Bibliog. 50). 'On indefinite quadratic forms in five variables’, with H. Heilbronn, 1946 (Bibliog. 49). 7pp. and 8pp. ms. drafts. H. Davenport CSAC 112/3/86 Publications "Theory of Numbers', 1946-47. Davenport was approached, initially by E.A. Milne, to write a book on this subject as one of a series of mathematical works for the interested layman. See D.89-D.92. 4 letters from E.A. Milne, 1946, outlining the proposed series, the level of mathematics to be aimed for and the publishers' terms. The book was published in 1952 as 'The higher arithmetic’. Letter from Hutchinson & Co., publishers, 1947, enquiring re Davenport's progress, with his reply apologising for the delay, due to pressure of work. 'The Natural Numbers’. Spp. typescript draft, probably of introduction to the book. 6pp. untitled typescript draft, paginated 15-20. ‘On the product of three non-homogeneous linear forms', 1947 (Bibliog. 52). 20pp. typescript draft, with ms. corrections. Letter to Heilbronn, 27 June 1946, re modification to a proof. 5pp. untitled ms. draft, partially paginated, labelled '55A'. little ‘Asymmetric inequalities for non-homogeneous linear forms', with H. Heilbronn, 1947 (Bibliog. 55). Included here is 'A problem in the geometry of numbers', with H. Heilbronn, 6pp. ms. draft labelled 'essentially published', probably 1947 or a later. 'final' draft. ‘On Hlawka's theorem in the geometry of numbers', with C.A. Rogers, 1947 (Bibliog. 58). Postcard from Rogers, 3 January 1947, re solution to an equation, and 3pp. ms. notes; Ilpp. ms. draft, Ip. labelled ‘Prelim to 58'; l0pp. ms. ‘Ona theorem of Markoff', 1947 (Bibliog. 57). Spp. ms. draft. H. Davenport CSAC 112/3/86 Publications 'The Geometry of Numbers', 1947 (Bibliog. 59). App. typescript draft. 'A historical note', 1947 (Bibliog. 60). 2pp. typescript draft with ms. corrections. "Non-homogeneous binary quadratic forms II', 1947 (Bibliog. 61). l4pp. typescript draft with ms. corrections. "Non-homogeneous binary quadratic forms III', 1947 (Bibliog. 62). 9pp. typescript draft. "Sur une extension d'un théor€me de Minkowski’, 1947 ‘Bibliog. 64). 2pp. ms. draft. D.47, D.48 D.47 D.48 24pp. ms. draft. 'The geometry of numbers', 1947 (Bibliog. 67). l0pp. typescript draft. 'Non-homogeneous binary quadratic forms IV', 1947 (Bibliog 66). Ilpp. ms. notes and calculations, Ip. labelled 'Prelim to 66'. App. typescript draft with ms. corrections. "Note on indefinite ternary quadratic forms', 1948 (Bibliog. 71). 'Non-homogeneous ternary quadratic forms', 1948 (Bibliog. 63). 34pp. ms. draft. H. Davenport CSAC 112/3/86 Publications 'On the equation ax? + by? +¢z2 = O', 1948 (Bibliog. 72). 5pp. typescript draft with ms. corrections, with Ip. ms. addition. 'On indefinite ternary quadratic forms', 1949 (Bibliog. 56) l4pp. typescript draft with ms. corrections, with Ip. ms. addition. 'On the product of two power series', with G. Pélya, 1949 (Bibliog. 69). 9pp. typescript draft; 10pp. ms. and typescript draft. ‘Ona result of Wald', with G. Pdlya, 1949 (unpublished). 2 ms. drafts, 6pp. and 5pp.; to Pélya. letter from Wald, 19 September 1949, 'A divisor problem', 1949 (Bibliog. 73). Ilpp. ms. draft. 'On a theorem of Khintchine', 1950 (Bibliog. 68). 18pp. typescript draft with ms. corrections. 25pp. typescript draft with ms. corrections. 'On the series for L(1)', 1949 (Bibliog. 73). 5pp. typescript draft with ms. corrections. "Indefinite binary quadratic forms, and Euclid's algorithm in real quadratic fields’, 1950 (Bibliog. 70). Continued 'Euclid's algorithm in real quadratic fields’, with H. Chatland, 1950 (Bibliog. 74) D.60 in certain real quadratic fields', by P. Varnavides. ‘A Theorem proving the existence of an Euclid's Algorithm 9pp. ms. draft, with letter, 18 May 1948, re publication of paper. H. Davenport CSAC 112/3/86 Publications D.60 (Cont'd.) ‘On the Euclidean algorithm in quadratic number fields', by H. Chatland. App. typescript draft, with letter, 28 May 1949, re queries made by Davenport . D.61 3pp. ms. notes and calculations. App. ms. draft entitled '3. Proof of the Theorem’. 'The field k (193)! 5pp. typescript draft, labelled 'sent to Chatland as a model for the calculation in 74'. D 62 'Euclid's algorithm and the class-number' 2pp. ms. draft. "Euclid's algorithm in real quadratic fields', l4pp. typescript draft. '"Euclid's algorithm in cubic fields of negative discriminant', 1950 (Bibliog. 76). D.64 D.65 13pp. ms. draft, labelled ' prelim to 77'. Ilpp. and 6pp. ms. drafts, both labelled 'prelim to 77'. ears "Indefinite binary quadratic forms', 1950 (Bibliog. 77). 23pp. typescript draft with ms. corrections, with 7pp. ms. additions. D.66 editor, T.W. Chaundy, re corrections. l2pp. typescript draft with ms. corrections, with note from Spp. typescript draft with ms. corrections. 'Diophantine inequalities with an infinity of solutions', with C.A. Rogers, 1950 (Bibliog. 79). ‘On the critical determinants of cylinders’, with C.A. Rogers, 1950 (Bibliog. 81). S9pp. typescript draft with ms. corrections; Ip. ms. list of contents. H. Davenport CSAC 112/3/86 Publications 'Euclid's algorithm in certain quartic fields', 1950 (Bibliog. 82). 34pp. typescript draft with ms. corrections. "Note on a binary quartic form', 1950 (Bibliog. 83). 10pp. typescript draft with ms. corrections. 'L'algorithme d'Euclide dans certains corps algébriques', Biblicg. 64), 7pp. typescript draft, in English, labelled ‘basis of lecture at Paris congress Sept 1949'; 9pp. ms. draft (in French). 1950 "Study and Research in Mathematics', 1950 (Bibliog. 85). 9pp. typescript draft. "Sums of three positive cubes', 1950 (Bibliog. 87). 6pp. ms. draft; 7pp. typescript draft. 15pp. ms. draft D.75 13pp. typescript draft with ms. corrections. ‘On a principle of Lipschitz', 1951 (Bibliog. 88). ‘Recent progress in the geometry of numbers', 1950 (Bibliog. 91). D.74 labelled 'Second draft (used at lecture)’ and 'Congress lecture’. Spp. ms. draft with 3pp. ms. notes; Spp- typescript draft labelled 'prelim to 88', with 4pp. ms. notes; 6pp. typescript draft. Ilpp. typescript draft. ‘On the class-number of binary cubic forms (1)', 8pp. typescript draft, entitled 'On binary cubic forms', labelled ‘preliminary to 89'; 1951 (Bibliog. 89). H. Davenport CSAC 112/3/86 Publications ‘On the class-number of binary cubic forms (II)', 1951 (Bibliog. 90). 7pp. typescript draft. "On sequences of positive integers', with P. Erdés, 1951 (Bibliog. 92). 6pp. typescript and ms. draft. "Prime Numbers', 1951 (Bibliog. 96). l0pp. typescript draft with ms. corrections. ‘Sur un systéme de sphtres qui recouvrent |'espace a n dimensions’, 1951 (Bibliog. 98). App. typescript draft, in English, entitled 'Note on a theorem of Rogers'; with covering note to Rogers, 22 May 1951, labelled ‘Preliminary to 98'; 3pp. typescript draft (in French). "Note on normal decimals', with P. Erdués, 1952 (Bibliog. 93). 8pp. photocopy of typescript draft. 7pp. ms. and typescript draft. 'The covering of space by spheres', 1952 (Bibliog. 99). 15pp. ms. and typescript draft. "Note ona result of Chalk', 1952 (Bibliog. 95). 12pp. photocopy of typescript draft. ‘Linear forms associated with an algebraic number-field', 1952 (Bibliog. 94). 20pp. typescript draft. 'The covering of n dimensional space by spheres’, with R.P. Bambah, 1952 (Bibliog. 97). H. Davenport CSAC 112/3/86 D.87 "Simultaneous Diophantine approximation', 1952 (Bibliog. 100). Publications l5pp. typescript draft with ms. corrections. 'The distribution of quadratic and higher residues’, with P. Erd&és, 1952 (Bibliog. 101). lépp. photocopy of typescript draft. D.89-D.92 'The Higher Arithmetic’, 1952. See also D.37. The book, which became a very popular textbook, reached its fifth edition in 1982. 'It has undoubtedly been a source of joy and inspiration to many mathematicians both amateur and professional’ (Memoir, p.167). See C.86 for cover illustration of fifth edition. D.89 ‘Old material for book'. Contents of a folder so inscribed, consisting of extensive ms. notes and drafts kept in their original order. clipped together for ease of reference. from 1947. Continuous sequences have been Some material probably dates D.90 lishers, 1951-57. Correspondence with Hutchinson's University Library, pub- Professor B. J. Birch has contributed (February 1986) the following explanatory note: Probably the material was "tested" in lectures at UCL (and maybe Bangor).' Correspondence with reviewers, L. Schoenfeld and P.T. Bateman, 1953, with Ip. ms. note of where reviews appeared. "All of this can be regarded as material for his book on "Higher Arithmetic", though only a small proportion of these notes survived into the printed version. Lew D.91, D.92 1952-61, arranged in alphabetical sequence. General correspondence with colleagues and others, D.91 B«~G DSe H. Davenport CSAC 112/3/86 Publications 'The minimal points of a positive definite quadratic form’, with G.L. Watson, 1954 (Bibliog. 103). Spp. typescript draft with ms. corrections. ‘Simultaneous Diophantine approximation’, 1954 (Bibliog. 104). 34pp. typescript draft. Mathematika, vol.1, part 1, June 1954. Davenport was responsible for the founding of this journal (see Memoir, p.164), and remained an editor throughout his life. contained 2 papers by him (Bibliog. 103 and 104). The first issue Proof copy with Davenport's ms. corrections, including Ip. ms. notes. ‘Simultaneous Diophantine approximation’, 1954 (Bibliog. 106). 5pp. typescript draft. 15pp. ms. draft. D.97 D.98 19pp. typescript draft with ms. corrections. D99*D, 101 2 letters from H.P.F. Swinnerton-Dyer, 1954, re publication Ds97,20 .98 "On a theorem of Furtwdngler', 1955 (Bibliog. 105). "Products of inhomogeneous linear forms', with H.P.F. Swinnerton- Dyer, 1955 (Bibliog. 107). D.99 of paper, with 2pp. ms. notes and calculations entitled 'n = 5, r= 1, s = 2', and labelled 're 107'. 44pp. typescript draft with ms. corrections. D.100 ‘first version’. D.101 33pp. untitled ms. draft (Swinnerton-Dyer's hand), labelled 5pp. untitled ms. draft, with 2pp. ms. calculations. H. Davenport CSAC 112/3/86 Publications "The solubility of certain Diophantine inequalities', with K.F. Roth, 1955 (Bibliog. 108). 24pp. paginated draft. ‘Rational approximations to algebraic numbers', with K.F. Roth, 1955 (Bibliog. 109). l5pp. typescript draft with ms. corrections. 'Le recouvrement de l'espace par des sphéres', 1955 (Bibliog. 110). 12pp. ms. draft. "Indefinite quadratic forms in many variables', 1956 (Bibliog. 112). 26pp. typescript draft with ms. corrections. "Note on irregularities of distribution’, 1956 (Bibliog. 113). 8pp. ms. draft. .107, D.108 =. See also D.112-D.120. D.107 34pp. ms. draft. D.108 Proofs, with ms. corrections. "Indefinite quadratic forms in many variables II', 1958 (Bibliog. 114). "Indefinite quadratic forms in many variables (III)', with B. J. Birch, 1958 (Bibliog. 118). 19pp. ms. draft (in Davenport's hand), labelled ‘superseded! . ‘On a theorem of Davenport and Heilbronn', with B.J. Birch, 1958 (Bibliog. 119). D.110 of "A theorem of Davenport & Heilbronn"'. 6pp. ms. draft (in Birch's hand), entitled 'Davenport's version 6pp. typescript draft, with ms. corrections by both authors. 310,011 See also D.112-D.120. H. Davenport CSAC 112/3/86 Publications D.111 37pp. typescript draft with ms. corrections. D.112-D.116 Correspondence with B.J. Birch, June 1957-July 1958, re joint papers (Bibliog. 118 and 119). Since Davenport collaborated with Birch on these two papers published in 1958, and as an accurate division of this material between them would be impossible, it has been arranged in a single chronological sequence. D.112 June, July 1957 D.115 January, February 1958 D.113 August 1957 D.116 March-July 1958 D.114 September -December 1957 D.117-D.120 Notes and drafts found with D.109-D.116, probably related to Bibliog. 118 and 119. i D.117 2 ms. drafts, 5pp. and IIpp. D.118 and 6pp. 2 ms. drafts on same subject, 7pp. (with 4pp. ms. notes) D.120 Ms. notes by Birch. D.122-D.128 D.122 7A4pp. ms. draft. D.119 Miscellaneous ms. notes, drafts and calculations. "Cubic forms in 32 variables', 1959 (Bibliog. 116). Spp. typescript draft with ms. corrections; set of page-proofs. 'The work of the Fields medallists. Dr. K.F. Roth’, 1958 (Bibliog. 121). "Absolute" lemmas’. 25pp. ms. draft, paginated 73-97, and headed '8 Synthesis’. D.123, D.124 different ms. corrections. 2 copies of 75pp. typescript draft, both with D.125 D.126 l4pp. ms. draft headed 'Cubic Forms. H. Davenport CSAC 112/3/86 Publications D.127 variables'; 26pp. ms. draft headed 'B. Ip. ms. notes headed 'History of cubic forms in 32 (later 16) Certain exponential sums'. D.128 lépp. ms. draft headed 'G. Synthesis’. (D.127, D.128 are the contents of a folder inscribed 'Cubic forms (old) historical interest’ .) D.129-D.131 "Indefinite quadratic forms', with D. Ridout, 1959 (Bibliog. 120). D.129 including Ip. in another hand. 8pp. ms. and typescript draft and notes, partially paginated, D.130 26pp. ms. draft. D.131 Set of page-proofs with ms. corrections. ‘Some recent progress in analytic number theory’, 1960 (Bibliog. 123). 12pp. typescript draft with ms. corrections; copy of J.Lond.Math.Soc., April 1960, including paper. 2 ms. drafts, 7pp. and 8pp. 2 ms. drafts, 15pp. and l6pp. "On a theorem of P. J. Cohen', 1960 (Bibliog. 125). 'Uber einige neuvere Fortschritte der additiven Zahlentheorie', 1960 (Bibliog. 127). ‘On Weyl's inequality and Waring's problem for cubes', with S. Chowla, 1961 (Bibliog. 124). 8pp. ms. draft 're 124' and 5pp. ms. draft. D.135, D.136 D.135 29pp. ms. draft. D.136 H. Davenport CSAC 112/3/86 Publications "A note on binary cubic forms', 1961 (Bibliog. 126). 2 ms. drafts, 9pp. and 1lpp; correspondence. ‘Equations of the form f(x) =g(y)', with D. J. Lewis and A. Schinzel, 1961 (Bibliog. 129). 13pp. ms. and typescript draft with ms. corrections. "Cubic forms in 29 variables', 1962 (Bibliog. 130). 23pp. typescript draft with ms. corrections. D.140, D.141 "The addition of norm forms', with B.J. Birch and D.J. Lewis, 1962 (Bibliog. 131). D.140 13pp. ms. draft. D.141 lépp. ms. draft, with 5pp. ms. notes. 34pp. ms. draft with covering note to 'Bryan' (Birch). D.145, D.146 D.145 D.146 'A note on Diophantine approximation’, 1962 (Bibliog. 133). 7pp. typescript draft with ms. corrections. "Cubic forms in sixteen variables’, 1963 (Bibliog. 134). Set of galley-proofs with ms. corrections. ‘Exponential sums in many variables', with D.J. Lewis, 1962 (Bibliog. 135). Set of page~proofs with ms. corrections; 2pp. ms. notes. "Notes on congruences (I)', with D. J. Lewis, 1963 (Bibliog. 136). 2 typescript drafts with ms. corrections, 9pp. and 12pp. H. Davenport CSAC 112/3/86 Publications "Notes on congruences (II)’, with D.J. Lewis, 1963 (Bibliog. 137). 15pp. ms. draft with corrections. ‘Homogeneous additive equations’, with D.J. Lewis, 1963 (Bibliog. 138). 46pp. ms. draft with corrections; note to publisher. 'A problematic identity’, 1963 (Bibliog. 140). 6pp. ms. draft. 'A note on Diophantine approximation (II)', 1964 (Bibliog. 144). 15pp. ms. draft with corrections. D.151, D.152 'Two problems concerning polynomials', with A. Schinzel, 1964 (Bibliog. 146). D.151 13pp. ms. draft; 12pp. typescript draft with ms. corrections. Spp. ms. notes by A. Schinzel, dated 9.3.64, possibly 'y2 - x3) 21965. D.154 version without corrections. 8pp. heavily-corrected ms. draft, and photocopy of original D. 154, D155 ‘On a theorem of Mrs. Turén', 1965 (Bibliog. 153). "Non-homog. cubic egns', with D. J. Lewis, 1964 (Bibliog. 148). D.152 work for this paper (or for Bibliog. 145). 10pp. ms. draft, beginning: 'This is an account of a paper by Lewis and myself which has been submitted to PLMS'. published as 159'. 6pp. ms. draft with 2pp. ms. notes, labelled ‘Early version, eventually too 7pp. photocopy of ms. draft with ms. corrections, and a covering letter to B.J. Birch, 8 July 1964. H. Davenport CSAC 112/3/86 Publications 7pp. untitled ms. draft, labelled 'm/s of 158 (first folio missing)’, 21966. "Looking back', 1966 (Bibliog. 162). lépp. typescript with ms. corrections. 'Small differences between prime numbers', with E. Bombieri, 1966 (Bibliog. 163). 33pp. photocopy of ms. draft, marked up for print. "A note on certain arithmetical constants', with A. Schinzel, 1966 (Bibliog. 165). 7pp. typescript draft with ms. corrections. ‘Cubic equations of additive type', with D.J. Lewis, 1966 (Bibliog. 167). 68pp. typescript draft with ms. corrections. "Notes on congruences. III', with D.J. Lewis, 1966 (Bibliog. 169). 'Eine Bemerkung Uber Dirichlets L-Funktionen', 1966 (Bibliog. 171). 17pp. ms. draft with corrections. 8pp. typescript draft, with Ip. ms. list of references and Ip. ms. calculations. ‘Diophantine approximation and sums of roots of unity', with A. Schinzel, 1967 (Bibliog. 166). Miscellaneous ms. notes and drafts. D.164 November 1965-October 1966. Correspondence, chiefly with A. Schinzel, re paper, .164-D.169 D.165 H. Davenport CSAC 112/3/86 Publications D.166 'A problem connected with Diophantine approximation’. 6pp. ms. draft. 'Diophantine approximation and roots of unity’. 8pp. ms. draft. D.167 21pp. ms. draft with corrections, labelled 'Versions of 166'. D.168 l5pp. ms. draft with corrections. D.169 additions. Photocopy of typescript draft, with ms. corrections and D.170-D.182 ‘Multiplicative number theory’, 1967. The book ‘contains an extremely readable account of the analytic approach to the theory of the distribution of primes in arithmetic progressions’ (Memoir, p.167). second edition (revised by H.L. Montgomery) did not appear until 1980. Davenport submitted a revised ms. in 1969 but the For related material see C.182-C.193. D.170-D.174 238pp. ms. draft with corrections. 5 folders. D.176, D.177 Corrected proofs. D.178-D.182 revised version. 5 folders. D.175 App. typescript index with ms. corrections. re corrections, also mentioning that he was in hospital. Photocopy of original ms. draft, with ms. corrections for D.178 includes letter from Davenport, 4 April 1969, to Yu. V. Linnik D.170 includes covering note from publisher, August 1967, returning "dead' material (now at D.170-D.177). For correspondence and further drafts see G.37. "On the large sieve method', with E. Bombieri, 1968 (Bibliog. 172). 17pp. ms. draft with corrections. H. Davenport CSAC 112/3/86 D.184, D.185 Publ ications 'On the representation of positive integers as sums of three cubes of positive rational numbers', with E. Landau, 1968 (Bibliog. 174). This paper was published in a memorial volume to Landau; the work had actually been done in 1935. D.184 5pp. and 4pp. Ms. notes and calculations, including 2 paginated sequences, 6épp. notes by Landau. D.185 Spp. ms. draft; corrected proofs. Also included is a letter from Marianne Landau on the death of her husband. D.186, D.187 "Bases for finite fields', 1968 (Bibliog. 175). D.186 Extensive ms. drafts and calculations. D.187 38pp. ms. draft with corrections. "A theorem on linear forms', with W.M. Schmidt, 1968 (Bibliog. 177). D.194, D.195 D.191 D.192 26pp. ms. draft. 23pp. photocopy of typescript draft. D.189-D.193 ‘A note on Thue's theorem', 1968 (Bibliog. 180). D.189 23pp. ms. draft 'Note on the Thue-Siegel Theorem’. D.190 3pp. ms. draft on ‘Siegel's Theorem’. 6pp. and Ilpp. drafts and calculations on 'Thue's Theorem’. rly . version of Bibliog. 181. ‘Some inequalities involving trigonometrical polynomials’, with E. Bombieri, 1969 (Bibliog. 181). ee photocopy of 'note on the large sieve inequality', with D.193 Corrected version of D.192 (photocopy). For correspondence re paper see G. 38. D.194 23pp. ms. draft. D.195 E. Bombieri. a H. Davenport CSAC 112/3/86 Publications D.196, D.197 ‘Correspondence with Baker relevant to 182, and twom/S'. Contents of a folder so inscribed. D.196 1967, re material for joint paper published in 1969 (Bibliog. 182). Three letters from Davenport to A. Baker, July, September (Information from Professor B. J. Birch, February 1986.) D.197 'The numerical determination of rational approximations’. 6pp. draft. "A non-homogeneous linear form in 2 variables’. App. ms. draft. ‘Approx. to a real number by alg-integers', with W.M. Schmidt, 1969 (Bibliog. 183). 6épp. ms. draft. ‘Simultaneous equations of additive type’, with D.J. Lewis, 1969 (Bibliog. 184). Correspondence, January, February 1969; 2pp. ms. draft. D.201-D.203 ‘On writing mathematical papers', 1969 (unpublished). See C.133, C.134 for Davenport's lecture material on Hardy. 105pp. photocopy of ms. draft with corrections; 4pp. ms. summary. Biographical article on G.H. Hardy commissioned by 'The Encyclopedia Americana’, 1969. and V. Armitage, February 1970. Letters to Mrs. Davenport re paper from J.W.S. Cassels, October 1969, 23pp. typescript draft with covering letter to Mrs. Davenport D.201 Correspondence, 1966, 1969; 2pp. ms. notes. D.202 Background material (printed matter). D.203 from L.J. Mordell, June 1969. H. Davenport CSAC 112/3/86 Publications "Two additive equations', with D.J. Lewis, 1971 (Bibliog. 186). 32pp. photocopy of typescript draft with ms. corrections. "Homogeneous quadratic equations’, 1971 (Bibliog. 194). 10pp. photocopy of typescript draft. ‘Gaps between values of positive definite quadratic forms', with D.J. Lewis, 1971 (Bibliog. 195). 27pp. photocopy of typescript draft; Ip. corrections. Ip. instructions to printer; 'Trigonometrical polynomials', published as 'The zeros of trigonometrical polynomials', Mathematika, 19, 1972, 88-90, with the footnote: 'This note has been prepared for publication by Professor H. Halberstam from a draft manuscript sent to him in 1967 by the late Professor Davenport in the course of a corres- pondence on the large sieve inequality; specifically, Halberstam had asked Davenport whether the inequality might not have some applications in the theory of trigonometrical polynomials and the note came in reply to this query.' : Reviews by Davenport, 1938-64. Arranged in chronological sequence by date of the publication of the work reviewed. 3pp. ms. note by Davenport; March 1968. letter from Halberstam returning it to him, Letter to Mrs. Davenport from C.A. Rogers, March 1972, enclosing photocopies of her husband's original draft and the proposed paper Halberstam had prepared from it. Davenport, n.d. Material includes review of L. J. Mordell's inaugural lecture as Sadleirian Professor at Cambridge, published 1947. 3pp. incomplete typescript draft of letter concerning a book, not by H. Davenport CSAC 112/3/86 Publications D.210-D.213 'The collected works of Harold Davenport', edited by B.J. Birch, H. Halberstam and C.A. Rogers, 1977. D.210-D.212 colleagues 1969-75. Correspondence between the editors and with other D.210 1969, 1970 D.211 1974 D.212 1975 D.213 by Davenport. B.J. Birch's ms. notes for and drafts of introductions to papers Photocopies of Davenport's typescript notes on his own work. for full version see A.10. Part only; App. typescript index, with ms. corrections by B.J. Birch. H. Davenport CSAC 112/3/86 SECTION E RESEARCH NOTES AND DRAFTS" E.1 - E.135 EUs -G tS COLLABORATION WITH HELMUT HASSE, 1933-36 Evl6 +£2.83 TITLED AND UNTITLED DRAFTS E.84 -E.102 MISCELLANEOUS NOTES AND CALCULATIONS E.103-E.126 NOTES ON WORK BY OTHERS E.127-E.135 §©=WORK BY OTHERS Est 1g COLLABORATION WITH HELMUT HASSE, 1933-36 Davenport visited Hasse in Marburg in the 1930s (Memoir, p.161) and they collaborated on a paper, published in 1934 (Bibliog. 8). Most of the material here is Hasse's work but there is some correspondence and a draft for a further collaborative Paper . Davenport's other collaborators are represented in Sections D and G. Bil eae 12pp. typescript and ms. draft with ms. corrections. E.1 1933, 1934 E.2 1935 For further correspondence with Hasse, see G.116-G.122. "Gaussian sums in finite fields', by H. Davenport and H. Hasse. Letters from Hasse, May 1933-November 1935, chiefly concerning the joint paper, mostly in English. 7pp. ms. draft, in German, by Hasse. E.4 includes sets of notes dated 28 September 1933 and 10 December 1935. Miscellaneous ms. notes and calculations by Hasse, in English and German. 2 folders. H. Davenport CSAC 112/3/86 Research notes and drafts Copies of typescript drafts of papers by Hasse, in German, presumably sent by him to Davenport. | Some have ms. corrections and some are dated, 1933-36. 9 folders. E,16-E -63 TITLED AND UNTITLED DRAFTS Probably many of these drafts were intended to form lectures or papers for publica - A number of these are untitled tion, while others may be no more than extensive notes. and very few are dated. Dated titled drafts ‘For a single irreducible polynomial’, 1934. Spp. ms. 'Tschebotareff's constant (/2)" 2pp. ms. with covering note to L. J. Mordell. "Three fourth powers', 1943. ‘Four fourth powers' (continuation of E.18). 6pp. ms. with Ip. ms. calculations. Folder also includes 2 additional, untitled drafts, each 3pp. App. ms., and 8pp. ms. labelled 'Revised version 17.10.43'. 7pp. ms. Folder also includes 3pp. ms. notes, found with above, entitled '5 4-th powers’. 'On X12 +5") 1946. H. Davenport CSAC 112/3/86 Research notes and drafts "Direct proof of Marshall Hall's Theorem', 1956. 2pp. ms., with 2pp. ms. entitled 'M. Hall. 9 May 1956. Difference sets', dated Undated titled drafts E.ez "Polynomials mod x4 7pp. ms. "Polynomials (mod p)’. App. ms. 'V inogradov's work on the addition of primes’. lépp. ms. "Primes in arithmetic progression’. 3pp. ms. with Ip. ms. notes. 9pp. typescript, with Ip. ms. notes. "Indefinite quadratic forms’. 18pp. ms., with Ip. ms. notes. ‘On reduced positive definite quadratic forms’. App. ms., with 10pp. untitled ms. draft and notes. 2pp. ms. with 3pp. ms. notes and calculations. 'The quadratic character’. "Characters (mod M)'. H. Davenport CSAC 112/3/86 Research notes and drafts 'The Weierstrassian equation y2 = 4x? - 92x ~93'- 6pp. ms. ‘On a problem of Fekete’. 3pp. ms. 'An introd. to Turén's book’. 10pp. ms. with reprint of paper presented by P. Turan and 6pp. ms. notes and calculations. 'Tur6n-Halész'. 6pp. ms. "Units: in algebraic number fields’. 10pp. ms., with bibliography. 9pp. ms. "Exponential sums’. Dirichlet Rome vol. to "Distribution of Farey fractions’. 13pp. ms. 'Diophantine equations in many variables’. 3pp. ms., found in an envelope labelled '185? appear', possibly an early draft for Bibliog. 185. ms. "On the cubic exponential sum'. 7pp. H. Davenport CSAC 112/3/86 Research notes and drafts "Notes on Littlewood's Problem’. 3pp. ms. with 4pp. ms. calculations. "Littlewood's Problem’. 2pp. ms. Included here is a further ms. draft, with notes, of the same title, and 3pp. draft on 'The distribution of certain fractional parts’. 'The critical lattices ...'. épp. ms. with Ip. ms. notes. 'The field k(/5)'. Spp. ms. "Units'. 10pp. ms., with 6pp. notes. ‘Four linear forms. Type I'. 3pp. ms. Opp. ms. 2pp. ms. ‘Binary cubic forms with D< O'. ‘Analytic treatments of the Kloosterman sums’. 'The product of three complex linear forms’. above. 2lpp. ms., with 4pp. ms. notes. Folder also includes '( ) of Type I', 13pp. ms. found with the H. Davenport CSAC 112/3/86 Research notes and drafts 'The congruence ...'. App. ms. 'A modification of Cauchy's inequality’. 3pp. ms. "Successive minima for Ly, ly, Lz". 2pp. ms. 'Macbeath's proof of Chalk's theorem’. Ip. ms. ‘Simplest version .of Rogers’. App. ms. "Ingham'. Spp. ms. 3pp. ms. "Quartic’. "Uniform distribution’. llpp. ms., with 10pp. ms. notes. "A lemma concerning pairs of integer points’. 2pp. ms., with 5pp. ms. notes and calculations. 5pp. ms., witha ms. note ‘Birch’. 'On the values of zeta (4 +it)’. H. Davenport CSAC 112/3/86 Research notes and drafts 'Modified definition of V,,'. App. ms. ‘Note on some conjectures of Ramanujan’. Ip. ms., paginated '102'. ‘Extension of Heilbronn's Theorem’. 13pp. ms., variously paginated, possibly connected with Bibliog. 176. 'Charaktere der Restklassengruppe mod (xk, p) 2pp. ms., in German. "Squares in A.P.'. 3pp. ms. E.63-E.65 These E.63 "Analytic continuation’. l5pp. ms. 'Various expansions and summations'; 8pp. ms. Shorter ms. drafts (some photocopies), with a ms. note 'copies sent to Don' (D.J. Lewis), kept together. paginated. All bear titles and most are Contents of an unlabelled binder, consisting of a sequence of unpaginated ms. drafts, possibly for a course of lectures, with some ms. notes. have been divided into separate folders for ease of reference, and kept in their original order. some paginated. l4pp. ms. 'The gamma function’; 22pp. ms. ‘Elliptic functions’. l1pp. ms. ‘Modular functions’; miscellaneous ms. notes, E.64 E.65 H. Davenport CSAC 112/3/86 Research notes and drafts E.66-E.68 ‘Miscellaneous math. mss and notes’. Contents of a binder so inscribed, consisting of miscellaneous ms. drafts, notes and calculations. into folders for ease of reference, and kept in their original order. | These have been divided Some with titles. 2pp. untitled (in another hand); E.66 6pp. 'Hermite's process of continued reduction'; 5pp. miscellaneous notes and calculations; 9pp. 'Cassels S.D.A.'. 3pp. untitled; 2pp. re '3 k-th powers', with covering 8pp. (in another hand) 'Markoff numbers'; 9pp. ‘Quadratic E.67 note; and higher residues'; 6pp. tables. App. on ‘various problems', E.68 2pp. notes, on ‘Simultaneous Diophantine Approximation'; 4pp. on 'On lattice points in n-dimensional star bodies'; 3pp. and Spp. un- titled. 13 October 1954; 4pp. with Miscellaneous bibliographies, including 2 with titles: 'Waring etc. in Math. Rev.' and 'Sieve methods’. In view Ei7tE 83 Untitled drafts Miscellaneous ms. lists of 'problems', probably intended to accompany undergraduate lecture courses. With the exception of E.71 and E.72, which contain typescripts, all the material here consists of ms. drafts without dates or titles. of the scantiness of the information available, no attempt has been made to describe these drafts in detail. 13 folders. H. Davenport CSAC 112/3/86 Research notes and drafts E.84-E.102 MISCELLANEOUS NOTES AND CALCULATIONS Notebooks E.84 Untitled notebook, with a few pages used at each end, containing miscellaneous ms. notes and calculations. Abundantes' . 1p. headed 'Numeri E’.85%E, oF 3 exercise books, labelled 'Cassels 1', 'Cassels 2' and 'Cassels 3', containing notes and calculations. E.88 Exercise book, labelled 'Math.', containing miscellaneous ms. calculations. Titled notes and calculations E.89 "Dyson's method for seven cubes’. App. ms., chiefly calculations, with 2pp. ms. calculations re article by Dickson. "Elaboration of previous argument’. 2pp. ms. ‘Ternary cubic’. 'Various equivalences between character-sums' . 12pp. ms. notes and calculations; 2 ms. tables entitled 'Properly primifive ternary forms’. Five items. "Zero of Emden Function’. 2pp. ms. notes. 2pp. ms. notes with 3pp. ms. calculations. Miscellaneous shorter notes, all titled. H. Davenport CSAC 112/3/86 Research notes and drafts Untitled notes and calculations E.95-E.102 Due to the dearth of information on these notes and calculations, no attempt has been made to describe them in detail. have been kept together; E.102 contains miscellaneous single sheets. Groups of notes E.98 contains material cleared from Davenport's office desk after his death (information from Professor B. J. Birch, February 1986). 8 folders. E.103-E.126 NOTES ON WORK BY OTHERS This material falls into two parts. Firstly, notes made by Davenport at lectures given by others (E.103-E.117) and secondly, notes made by him on a particular publica- tion, or line of work, of another (E.118-E.126). Notes at lectures E.103 Ip. ms. notes. Contents of a folder so inscribed. E.104 1951-52 Seminar talks and lectures by P. Erdds. E.104-E.117 "Lectures attended', 1951-63 and undated. ‘Lecture attended in Brussels on Alternating Algebra, May 1946'. E.105 C.A. Rogers, H.A. Heilbronn. A. Oppenheim. Lectures by K.F. Roth, K. Mahler, J.H.H. Chalk, Seminar talks and lectures by K. Mahler, L. Few. Seminar talks and lectures by K. Mahler, P. Erdés, Lectures by W.B. Pennington, B.J. Birch, E.106 C.A. Rogers. 1953 Lectures by T. Estermann, A. Renyi. 1952 1954 1955 1956 E.107 E.108 E.109 H. Davenport CSAC 112/3/86 Research notes and drafts .110 1956-57 Lectures by W.B. Pennington, J.W.S. Cassels, P.. Erdés, G.L. Watson. 111 .112 2913 1957 Lectures by G.C. Shepherd, Danicic, W.J. LeVeque. 1958-59 Lectures by L.J. Mordell, P. Erdés, A.E. Ingham. 1960-63 Lectures by B.J. Birch, K. Mahler, P. Erd&s. 114 . Few, Gelfond. n.d. Seminar talks and lectures by E.S. Barnes, P. Erd&s, e116 nds Lectures by H. Halberstam, K.A. Hirsch, K. Mahler. E.116 G.L. Watson. n.d. Lectures by C.A. Rogers, K.F. Roth, C.L. Siegel, e117. Shorter unidentified notes. Included here is Mrs. Davenport's list of contents of material now at £.103-E. 117. Davenport's notes on work by others E.118, E.119 Material relating to Blichfeldt, collected or made by Davenport. E.118 2 letters from A. Braver, 1932, to Blichfeldt. Although in many cases Davenport gave the date of publication of the work, few of these notes are themselves dated. Therefore they have been arranged in alphabetical order, with the exception of E.125, E.126, where the contents of one of Davenport's own folders have been kept together. Ms. notes, some dated 1920-22, not in Davenport's hand. 6pp. typescript draft of a lecture by Davenport, containing material on 'Blichfeldt's Principle’. 4pp. miscellaneous ms. notes on Blichfeldt, made by Davenport, n.d. (c.1947-50). "Various topics in the theory of numbers', 1953-54. See also C.27-C.29. "Remarks on work of Blichfeldt', n.d. (c. 1947-50). 2pp. ms. notes by Davenport. Sete H. Davenport CSAC 112/3/86 Research notes and drafts E.120 ‘Richard Braver. A note on systems of homogeneous algebraic equations’, n.d. 3pp. ms. on paper published by Braver in 1945. " Jacobi’, n.d. 8pp. ms. draft and Ip. ms. calculations. "Mordell's work', n.d. App. ms. 'Polya's Problem in Amer, Math Monthly', n.d. 3pp. ms. on paper by G. Pélya. ‘Rademacher. Riemann-von Mangoldt Theorem', 7 July 1959. Spp. ms. 'R. Remak. Formen’. Uber die Minkowskische Reduktion der definiten quadratischen 3pp. ms. on paper published by Remak in 1938. 'J.V. Whitworth’, n.d. 6pp. ms. on paper published by Vinogradov in 1927. Ip. ms. notes re Whitworth's thesis, 1947, for MSc. at Manchester University. 'J.M. Vinogradov. Ona general theorem concerning the distribution of the residues and non-residues of powers', n.d. Ms. notes on Lerche's formula. Ms. notes on work by Hecke, including 'Uber analytische funktionen und Verteilung von Zahlen mod eins' (published 1921). E2125 Ms. notes on various topics made from Hardy -Littlewood. Gti26, £.126 "Miscellaneous math mss’. Contents of a folder so inscribed. H. Davenport CSAC 112/3/86 Research notes and drafts beled analytische Zahlentheorie'. ‘Landau. Bedeutung der Pfeifferschen Methode flr die Ms. notes on paper published by E. Landau in 1912. 3pp. ms. notes, headed 'B.M. Wilson’. 7pp. ms. notes aiid calculations. E.127-E.135 §©WORK BY OTHERS In alphabetical order. Of special interest is E.131, a selection and discussion of research problems by J.E. Littlewood, and Davenport's comments on them. ety, 'A valuation of some information concerning finite fields', by J.H. Conway, n.d. l4pp. typescript. (Information from Professor "Research Problems’, by H.T. Croft, August 1967. 28pp. duplicated typescript. "Problems (mostly geometrical)', by H.T. Croft, n.d. 'This set of problems went through various editions, and was published (in collaboration with R.K. Guy) in ¢.1983, under the title "Unsolved Problems in Intuitive Mathematics"'. B.J. Birch, February 1986.) 7pp. duplicated typescript. H. Davenport CSAC 112/3/86 Research notes and drafts E.129, E.130 Duplicated copies of early ms. drafts by A.E. Ingham of his 'Cambridge Tract', published in 1932 as The distribution of prime numbers. B.129 E.130 'The Theory of the Distribution of Primes. Chapter I', n.d. ‘Chapter I', n.d. "Research Problems’, by J.E. Littlewood, n.d. Duplicated manuscript; 4pp. introductory material beginning 'This is for "Family" reading, aimed at present and former pupils ...' explaining purpose and history of selection of problems; 26pp. list of problems. The document is accompanied by Davenport's 2pp. typescript, 'Comments', n.d. "Difference of two positive definite quadratic forms', by D. Ridout, n.d. (4pp. ms.). Miscellaneous ms. notes by C.A. Rogers, n.d. Photocopies of ms. drafts by H.P.F. Swinnerton-Dyer, n.d. Unidentified. H. Davenport CSAC 112/3/86 SECTION F FACULTY OF MATHEMATICS, CAMBRIDGE F.1 - F.17 Fr. St 6 Esser? GENERAL COMMITTEES NEEDS OF FACULTY AND SUB-DEPARTMENTS F.10-F 42 APPOINTMENTS, 1960-69 Fale REQUESTS FOR POST-GRADUATE PLACES F.14-F.16 EXAMINATION PAPERS rat MISCELLANEOUS GENERAL COMMITTEES, 1959-65 Policy Committee of the Faculty of Mathematics, 1959-64. Notices of meetings, agendas, minutes and reports, arranged in chronological order. Be 1959-60 Bao 1964-65 and n.d. Pure Mathematics Lectures Committee, 1962 Notice of meeting and proposals for lecture list. Faculty Board of Mathematics, 1964-65. F.6 : 1961-63 Correspondence and committee minutes, mainly re newly- eo created Department of Applied Mathematics and Theoretical Physics (D.A.M.T.P.). October 1964. Notes and correspondence re affairs of D.A.M.T.P., H. Davenport CSAC 112/3/86 Faculty of Mathematics, Cambridge NEEDS OF FACULTY AND SUB-DEPARTMENTS, 1959-65 These papers largely consist ments, in various areas, such as teaching staff, new equipment, etc. of Statements of Needs of various depart - 7 1959-60 F.8 1961-64 ye 1965 and n.d. Fr AOcF 12 APPOINTMENTS, 1960-69 This material largely consists of papers of the Appointments Committee of the Faculty of Mathematics. vacant posts, applications, requests for curricula vitae, etc. There is also a little correspondence re F.10 1960-61 eae 9G ae 1963-69 In alphabetical order, 1964, 1965 only. B.14-F 216 EXAMINATION PAPERS REQUESTS FOR POST-GRADUATE PLACES Diophantine Approximation Copies of examination papers for Mathematical Tripos, Part III, 1964 and 1967. 2pp. ms. list of examination questions, with covering letter from J.W.S. Cassels, 1961, re suitability of one question. 2pp. untitled ms. list of examination questions, n.d. F.14 F.15 1964 1967 Papers | - VI Paper 13. H. Davenport CSAC 112/3/86 Faculty of Mathematics, Cambridge MISCELLANEOUS Shorter items, 1964, 1966 and n.d. Includes letter and 3pp. report re Science Research Council funded project on 'Equations in many variables’, 1966. H. Davenport CSAC 112/3/86 SECTION G CORRESPONDENCE G.1 - G.373 Although there are several substantial exchanges, many of the letters are incoming only, sometimes with a brief ms. note by Davenport of his reply (presumably sent in long- hand) on which ensuing correspondence may be based. The content is essentially mathematical though some personal news from Davenport's long-term friends, colleagues and pupils may be included. Of special interest are the extensive exchanges with E. Bombierj, H.A. Heilbronn, K. Mahler and L.J. Mordell, while no correspondence with G.H. Hardy, however brief, lacks its characteristic quality. Davenport's long association with German mathematicians, many of whom became refugees in British universities including Cambridge, is well documented; several of the sequences are wholly or partly in German. Mrs. Davenport's notes identifying correspondents and their connections with Davenport often accompany the letters and have been gratefully drawn upon in compiling the entries. Adams, A 1956, 1959-60 1948-52, 1958 Aitken, A.C. Inequalities. Ankeny, N.C. Mainly on number theory. Mathematical puzzles on integers. A research student of Davenport at Stanford 1947-48, later at Princeton and M.1.T. 11pp. 'Notes on a Sunday Times brain teaser’. Ap Simon, H.G. n.d. probably 1957 H. Davenport CSAC 112/3/86 Corresponden ce Or.7 Armitage, J.V. 1955-68 A research student of Davenport, later at King's College, London, and Durham. General correspondence on research, appointments, publications. G5 G.6 G7 1990757 1958-61 1962-68 Atkin, A.O.L. Austin, M.C G.10-O12 Bambah, R.P. 1946, 1961, 1964 1951 1950-61 Bambah, an Indian mathematician, studied with Davenport in London and published a collaborative paper with him in 1952 (Bibliog. 97). G.10 1950-53 1961, 1965 (a letter from a pupil of Bambah on mathematical 1949, 1964 1947, 1966, 1968 G.12 result). Barnes, E.S. Basu, S.K. 1954 G.11 Arrangements for Bambah's Fellowship at St. John's College, Cambridge; includes list of publications and draft paper on 'Four Squares’. list of publications, etc. 1933-34, 1939 A German mathematician who was obliged to leave for Britain in 1939. 1950 letter is re paper by R.P. Bambah (q.v.). Correspondence 1963-65 is on general research problems, appointments, publica- tions, etc. Correspondence 1939 includes curriculum vitae, testimonials, A student of Davenport in London, 1945-47. Bateman, P.T 1950, 1963-65 Behrend, F.A. H. Davenport CSAC 112/3/86 Correspondence Berlowitz, B. 1967 Besicovitch, A.S. 1943, 1947-48, 1950, 1955, 1959 Davenport had been a pupil of Besicovitch and succeeded him as Rouse Ball Professor at Cambridge. for the award of the de Morgan medal to Besicovitch (not signed). 1950 document is recommendation Billing, G. 1939, 1940, 1942, 1952 A Swedish mathematical and bridge-playing colleague at Manchester. Birch, B. J. 1959, 1966 Brief correspondence only. he contributed an account of his 'Work on the frequent collaborators; analytic theory of diophantine equations’ to the Memoir (pp. 171-176) and was an editor of the posthumous 'Collected Works’. Birch was one of Davenport's most G:21-G,23 Blaney, H. 1947-54 A research student of Davenport at London. 2.21 and publication. 1947, November-December. Frequent letters on results October-December. Blundon, W.J. 1956-57 G.22 paper G.23 1949, 1953-54. 1948, January-July. Similar correspondence, includes draft Mainly publication of Blundon's papers on ‘multiple covering’, and ‘packing'; includes figures. of studies' during year at Cambridge. Mainly arrangements for Bollobas to come to Trinity College for academic year 1963-64 and including Davenport's recommendation and ‘account Davenport's publications in Acta Mathematiea. 1948 1947, 1949 Boas, R.P. Jnr. Bohr, H Bollobas, B. 1963-65, 1967 H. Davenport CSAC 112/3/86 Correspondence G.28-G.39 Bombieri, E. and others 1963-74 Bombieri, an Italian mathematician working at Milan, Pisa and Princeton, visited Davenport in 1963 and 1964 and published four collaborative papers with him (Bibliog. 150, See Memoir, pp.164-165). 163, 172, 181. 1963-64 G.28 in Cambridge 1963-64 and arrangements for Davenport to lecture in Milan. Includes Davenport's report on Bombieri's work G.29 lations; Dirichlet L-functions’. 1965, January-July Correspondence, notes and calcu- includes draft paper by Bombieri on 'The Statistical theory of G.30 (published Proc .Roy.Soc. A, 1966). 1965, August Correspondence and drafts on primes paper G.3]1 one each by Davenport and Bombieri, related to correspondence. ‘Small differences of primes', two ms. drafts, 1965, August G.32 and drafts, (published 1968, see G.38). 1965, September-December on ‘prime numbers' paper and on ‘large sieve’ paper Continuing correspondence G.33 G.34 G.35 G.36 1967 1968, January-July 1966, January-April 1966, June-September 1966, October-December Mainly on sieve paper. Includes letter from H. Halberstam. Includes revised version of 'large sieve method' July, Extensive notes by Davenport kept with 1966 correspondence. G37. and correspondence on polynomials (leading up to collaborative paper published in 1969). G.38 of ‘large sieve’ paper, and a 7pp. ms. by Davenport 'The case N§ small’, and letters of comment. Fields medal at International Mathematical Congress, Vancouver, 1974. Also includes press-cutting re award to Bombieri of the Includes arrangements re publication G.39 1969 H. Davenport CSAC 112/3/86 Correspondence Bosanquet, L.S. Brandon, R.W. 1948, 1949 1953 Braver, A. 1931, and Braver, R. 1953 Brothers, both German refugee mathematicians. Brjuno, A.D. Broadbent, A. Brown, D.S. 4-colour problem. Buckell, J.F. Four Square Representation. Buhl, G. 1954 1934 Burt, C. Capildeo, R. Bullen, K.E. Burgess, D.A. 1963, 1965, 1968 Correspondence A former research student. One letter only. Printing of journals and especially Mathematika. A former research student of Davenport at U.C.L. on 'character sums'. Continued Cassels, J.W.S. General correspondence on research and publications. November-December 1946, 1947 G.54 1954, 1955, 1956 G.52 i353 1948, 1949, 1951 G .52-G..56 1946-69 and n.d. H. Davenport CSAC 112/3/86 Correspondence G.55 1963, 1969 Undated; includes sequences of ms. notes by Cassels, G.56 perhaps 1950s, and contents list of proposed book by him titled "An introduction to the geometry of numbers’. GChalk,..J.H.H. A former research student of Davenport in London. is addressed to C.A. Rogers. 1947, 1950, 1969 Letter of 1947 Champernowne, A. n.d. 1946-48, 1964 On functional equations; also includes some Chandrasekhar, S. G.59 personal news. 1946-48 G.60 1964 Chase, R.E. Proof of unique factorisation. 1933-63 The surviving Chételet, F. Chatland, H. 1946 1948-49 Chowla, S. Mainly on collaborative paper (Bibliog. 74). Chowla, a distinguished Indian pure mathematician, studied at Cambridge, where his supervisor was J.E. Littlewood. academic posts in India, moving to USA in 1948. correspondence is sporadic and does not include any of Davenport's replies. 1962, 1963. Mainly re collaborative paper (Bibliog. 124), 1933-34 andn.d. —_ Includes testimonials for Chowla G.64 from J.E. Littlewood and G.H. Hardy. has a ms. note 'Chowla to Walfisz' (see G.335). material may be from Chowla's earlier period at Cambridge. Letter of 16 February 1933 Some of the undated He returned to - G.65 G.66 1947-49 1958-60 H. Davenport CSAC 112/3/86 Correspondence Cohen, P.J. Research and publications. G.68, G.69 Cohn, H. 1959, 1960, 1965 1948-54, 1960-62 G.68 1948-54 Research and recommendations. G.69 for L. J. Mordell. 1960-62 Mainly re proposed 75th birthday symposium Cole. Ai. A research student of Davenport in London; mainly re thesis. 1952-53 Collingwood, E. Centenary of London Mathematical Society; article on subject by Collingwood. 1965 includes reprint of 1934, 1945, 1947 Courant, R. Early correspondence is from G&ttingen, with news of German mathe - maticians. is renewing contact after the war. Courant left for America in August 1934. Later correspondence 1928-59 1939 1945-48 G.73-G.76 Coxeter, H.M.S. G.74 G75 1928, 1929, 1932 (from Coxeter's mother), 1935. Includes G.73 3pp. 'Prop' by Coxeter. Includes some personal news as well as mathematical research. An undergraduate friend of Davenport at Cambridge, using his youthful nickname of 'Dave' in the letter of 1928 and signing his own letters 'Donald'. and passed on by him to Davenport. Packing of small circles. Enquiry originally addressed to S.T. Shovelton G.76 1951-53, 1958459 Cridland, N. 1954-56 H. Davenport CSAC 112/3/86 Correspondence G.78 Davies, M. 1947 A research student of Davenport on his visit to Stanford. Davis, C.S. 1945, 1949, 1955 de Bruijn, N.G. 1951-52 1955 Correspondence 1951-52 is re suitable prize problem for Amsterdam Mathematical Society. Delaunay, B. Derry, D. Minkowski's work. Dirac, G.A. and others Dolciani, M.P. 1963 1938 1964-65 1953-55 G.84 Davenport on theory of numbers. Arrangements to spend sabbatical leave working with Dyson, F.J. Eichler, M. 1962 DuVal, P. 1935 Draim, N.A. various dates 1950-65 G.85 Miscellaneous ms. notes and drafts. One letter only, from Princeton. Mainly mathematical but refers to J. von Neumann's proposed visit to Cambridge. 1942, 1946 Includes laudatory report by Davenport on 'fellowship thesis by F.J. Dyson: "Two problems in the theory of numbers".' Elliott, P.D.T.A, One letter only. H. Davenport CSAC 112/3/86 Correspondence Ennola, V. 1957-59 Research, draft paper on lattice constants. Erdds, P. 1934, 1960, 1961-65, 1969 Although Erd&s and Davenport collaborated on many publications 1936-63, the surviving correspondence is very meagre and is mainly from Erdés on various mathematical discoveries. Correspondence 1960 is enquiry re Erdds's problem on sets of congruences. Errera, A. Estermann, T. Davenport's ms. letter only. Evelyn, J. Fenna, D. 1953, 4955 1949 1950, 1960 1958 Paper on ‘Simultaneous diophantine approximation to series’. Godwin, H.J. Goodstein, R.L. Flanders, H. Flett, T.M. 1969 1949-50 Fjellstedt, L. Davenport's carbon only, on a paper by Fjellstedt. 1956 Davenport's unpublished 1938 work on inhomogeneous linear forms. Brief exchanges only. Appreciation of Davenport's paper 'Study and research in mathematics' (Bibliog. 85). 1955 1950 1939 1958, 1964 1947, 1952, n.d. Grunwald, G. Guy, R.K. Hadamard, J. H. Davenport CSAC 112/3/86 Correspondence Halberstam, H. 1957, 1962-68 Research, publications, appointments. Haldane, J.B.S. 1952 One letter only, on an inequality, with Ip. attached calculations by Davenport headed 'Haldane'. Hall, M. 1947-48, 1958 General correspondence on research and publications, including collaborative paper (Bibliog. 72). Hall, P. One letter oly. G.109-G.114 Hardy, G.H. 1965 1938-47 Hardy, one of the most distinguished British mathematicians of his day, was Sadleirian Professor of pure mathematics at Cambridge 1931-42. Although this did not coincide with Davenport's undergraduate period, he and Hardy were colleagues at Trinity during the 1930s and they collaborated on a second edition of 'Hardy-Wright' (An Introduction to the Theory of Numbers, by G.H. Hardy and E.M. Wright, 1938), see G.112, G.113; see G.351 for brief correspondence re 3rd edition. G.109 1938, 1939 Appeal on behalf of H. Heilbronn. G.111 undergraduate here called Dyson who is very promising’ [F.J. Dyson]. 1941, n.d. — Undated letter (perhaps 1942) refers to 'an Hardy's communications are letters and cards in his distinctive spiky handwriting, often with parentheses and balloons of afterthoughts, some in pencil and few dated other than by postmark. 1945, 1946, 1947 G.112 of 'Hardy-Wright' but including a little general mathematical information. 1944, May~December and undated. o.4113 October, and miscellaneous comments on other parts of book. Davenport's letter and revision of Chapter 24, 1944 Mainly on revisions G.110 1940 G.114 H. Davenport CSAC 112/3/86 Correspondence Haselgrove, C.B. One letter only, on mathematical tables. G.116-G.122 Hasse, H. 1932-52, 1963, 1967 Hasse was a distinguished German mathematician who invited Davenport to work with him in Marburg (see also G.209); Hasse was director of the Mathematical Institute in Géttingen 1934-45. his work greatly though they did not agree on political matters. pre-war letters are all in very fluent English, with some personal and general as well as mathematical news. His letters in German use the ‘du’ form right to the end. Davenport admired Hasse's G.116 1932, November, December Gey by G.H. Hardy. 1933, January-June. Letter of 20 January has a ms. note 1933, July-December. G.118 and 11 November include news of German mathematicians in Germany and abroad. Hasse's letters of 20 and 24 October G.119 joint paper (Bibliog. 8), and Hasse's appointment at G&ttingen. Includes material re Hasse's and Davenport's 1934 G.123-G.142 1934-67 GAZ G.122 G.120 1935 Heilbronn, H.A. and others 1936, 1938, 1939 1946, 1947, 1949, 1952, 1963, 1967 (death of Hasse's wife). Continued Heilbronn, a German-Jewish mathematician, was a life-long friend of Davenport, a colleague at Trinity College, Cambridge, and at University College, London, and a collaborator on many papers. was forced to leave Gittingen in 1933, Davenport seems to have initiated the moves to help him find a post in Britain, and when he was temporarily interned as an ‘enemy alien’ in the Isle of Man in 1940, it was Davenport whom Gertrud Heilbronn (mother of Hans) appointed to be in charge of her affairs (G.125 and see also G.110 for an appeal by G.H. Hardy on behalf of Heilbronn). friendship with Davenport, can be found in the Memoir by J.W.S. Cassels andA, Frdhlich (Biographical Memoirs of Fellows of the Royal Society, 22, 1976), an offprint of which is included at G.123. — A fuller account of Heilbronn's career, including his When Heilbronn H. Davenport CSAC 112/3/86 G.123-G.142 (Cont'd.) Correspondence G.123 only, re Heilbronn's acceptance of Bevan Fellowship at Trinity). Includes a letter from L.J. Mordell; 1934 1935. (card G.124 1939 Two letters only. C125 family affairs, release and service in army. 1940 Includes correspondence re internment, Heilbronn's G.126 help for Heilbronn's parents, tentatively dated 1943 by Mrs. Davenport. Includes undated letter from G.H. Hardy re 1946 Research, publications (Bibliog. 54). G.127 G.128 G.129 G.130 1947 1948 1949 1950 G.13]1 draft' for a paper 'On cubic fields' by Davenport. 1951-54 ~=Includes various notes and drafts and a ‘Rough G.132 1955-58 Research, publications, appointments. In 1963 Heilbronn resigned from his University expansion and shortage of mathematical teachers Heilbronn disagreed with the proposed large increase in undergraduate numbers, feeling that standards of entry and of teaching would fall. Davenport shared this view and helped to organise questionnaires for information from university colleagues, formulate memoranda and make representations on the subject. Chair at Bristol and left Britain for USA and Canada (see Memoir, pp. 122, 124-25). Almost all the documents in G.133-G.140 are concerned with the question of university expansion, but there are also a few references to the affairs of the London Mathematical Society and the Mathematical Tables Committee. and Davenport. G.134 to Chairman, U.G.C, (Sir Keith, later Lord, Murray) and draft questionnaire. G.135 university teachers in mathematics' circulated April 1960 by Heilbronn Material re 'Questionnaire on recruitment of G.133 headed 'University expansion. Heilbronn's letter to A.U.T., December 1959, Includes draft letter and memorandum 1959 1960 Quantity or quality’. 1960, January-March. H. Davenport CSAC 112/3/86 Correspondence G.136 Cambridge, sent to Davenport in answer to questionnaire. Replies and information from colleagues in 1960, May 54137 tinuing correspondence, including a little on affairs of L.M.S. Tables of results and information, and con- 1960, May G.138 university expansion, to be sent to U.G.C. 1960, June-July © Mainly re "Second Memorandum’ on 1960, June-July | Correspondence re proposed conference Davenport was asked to chair G.139 on shortage of teachers of mathematics. the conference but declined because of his views on university expansion. (Correspondence kept with the Heilbronn material. ) G.140 Memorandum', 'Notes on the questionnaire’, etc. Miscellaneous notes and drafts for 'Second 1960 G.14] 1962-63 G.142 1964, 1965, 1967 Brief correspondence only. Heinhold, J. 1948 1963 1952 Hlawka, E. Henstock, R. Hirsch, K.A. Hodge, W.D.V. 1948, 1952-56, 1962, 1963 General correspondence on research and publications, and some personal. Includes (1963) humorous poem 'To Professor Mordell on arrival to the city of Vienna’. 1955, 1958 Correspondence 1954 is re P. Erdus. Hofreiter, N. Hooley, C. Hopf, H. 1954, 1965 195] 1963, 1965 H. Davenport CSAC 112/3/86 Correspondence Hua, L-K 1939, 1940, 1949, 1964 Later President of Academia Sinica. G.152, G.153 Ingham, A.E. and others 1950 G.152 volume of essays on G.H. Hardy. 1950 Correspondence with Ingham and others re G.153 1950, 1954, 1956, 1960, 1963 Inkeri, K. Quadratic forms. G. 156-G.. 157 Jaeger, J.C. 1948-49 1936-57 A friend of Davenport at Cambridge in 1930s before returning to Tasmania and (from 1951) Canberra. Early letters are addressed to 'Dave'. 155 1936-44 G.156 1945-48 G.157 1950, 1957 Jarnik, V. Jenkins, G.M. Kanagasabapathy, P. 1951-52, 1962-63, 1968 1946 1961 Research and publications. On 'Physics teaching in Britain’. A Czech mathematician, renewing contact with UK colleagues. Polish research student at Cambridge. Letters to Davenport in California, with news of UCL and Britain. Khan, N.A. Knapowski, S. 1954 1959, 1963, 1966 Kemmer, N. Kestelman, H. 1947, 1948 H. Davenport CSAC 112/3/86 Correspondence Kober, H. 1934-35 and undated, 1942 A German refugee mathematician. Breslau, correspondence 1942 from Birmingham. Correspondence 1930s is from Kosambi, D.D. Kreisel, G. Lang, S. 196] 1958 1963-64 Comments on Davenport's research notes and publications. Ledermann, W. 1958 Includes 6pp. ms. note by Davenport 'A question concerning quadratic forms’. .170 ATI Leech, J. Lehmer, D.H. 1958 1948 .172, G.173 LeVeque, W. J. 1961, 1963 1961 Correspondence on proposed 'Compilation of a G.172 Topical History of the Theory of Numbers'. report (not favourable) of American Mathematical Society Committee, Davenport's draft comments, etc. Includes draft proposal, 1963 Levy, M. Includes 6pp. ms. note by Davenport, 'On Weyl's G.173 criterion for uniform distribution’ later published jointly with LeVeque and Erdts (Bibliog. 142) anda related note by LeVeque on Weyl's criterion. Delay lines. 1950 H. Davenport CSAC 112/3/86 G.175-G.184 Lewis, D.J. 1957-68 Correspondence Lewis, a professor of mathematics at Ann Arbor, Michigan, was a close friend and frequent collaborator on papers, some published after Davenport's Much of the correspondence reflects their friendly and hospitable death. relationship as well as research, visits and publications, and general news of the mathematical scene. A little correspondence from Carolyn Lewis is included. See also C.115-C.129. G.175 1957-58 (Bibliog. 116). G.176 1959-60 G 17 196] G .178 1962 (Bibliog. 137, 139), visits, lectures G 479 1963 (Bibliog. 138, 139, 141, 145) G .180 1964 (Bibliog. 148) : G.181 1965 1952+53,. 1955 1931 G . 183 S. 184 G . 182 1966 (Bibliog. 169) 1967 1968 Linnik, Yu. V. Littlewood, D.E. 1950-69 (not all dated) General correspondence, including Russian translation of Davenport's Multiplicative number theory. Card only. Littlewood, J.E. H. Davenport CSAC 112/3/86 Correspondence G.188, G.189 London Mathematical Society 1952-53 Correspondence and papers November 1952-January 1953 re finances, publishing policy, etc., with Treasurer of the Society, Royal Society, colleagues, etc. G.188 Correspondence, notes for meetings. G.189 Minutes, accounts, background information. G.190 McAndrew, H. G.191 Macbeath, A.M. G.192 Mack, J. G.193 McLeod, J.B. 1959 n.d. 1963 1963 G.194-G.201 Mahler, K. ; 1933-67 Mahler, a refugee German mathematician, was a colleague of Davenport at Manchester (where L.J. Mordell had obtained support for him) and a long-term friend. G.196 1947-49 Gr 197 1990-51, 1953 G.195 1945 (Bibliog. 47), 1946 Includes some reference to the founding of, and G.194 Mahler was interned). G.198 papers for, Mathematika. 1954-55 1933-34, 1940 (one letter only, from Isle of Man where (one letter only). G.201 Letter of 4 March 1963 announces Mahler's decision to accept research chair at Australian National University, Canberra. G.200 1958-59, 1961 G.199 1956-57 1962-63. 1967 H. Davenport CSAC 112/3/86 Correspondence Mann, H.B. Matthews, K.R. Mayer, A. n.d. 1963-66 1950 A German refugee, thanking Davenport for help with publication . Mendelsohn, N.S. Milne, E.A. 1949 1926-27, 1945 Milne was Davenport's tutor in applied mathematics at Manchester, 1924-27. Letters of 1926-27 are re Davenport's Scholarship at Trinity (Milne's own college, to which he was devoted), with advice on directions of study. Letter of 1945 is on current leaders in mathematics. . G.207 Montgomery, H.L. G.208-G.232 Mordell, L.J. 1969 1927-68 The Manchester Mordell succeeded Hardy in the Sadleirian Chair at. Mordell, a distinguished mathematician of American origin, witha special interest in number theory, was Fielden Professor of Mathematics at Manchester when Davenport took his first degree there. school of mathematics was particularly strong in the 1930s, and included several refugee mathematicians; Davenport also joined it as Assistant Lecturer in 1937. Cambridge 1945-53 and remained in contact with Cambridge mathematics until his death in 1972. Davenport was among his closest friends. Mordell recognised his quality from a very early stage (see G.208), helped him to share his own special interest in the geometry of numbers, and, according to J.W.S. Cassels, looked on Davenport as ‘his spiritual heir' (Biographical Memoirs of Fellows of the Royal Society, 19, 1973, pp -493-520). teach English to Hasse. The later correspondence (from about 1944, when Christian names began to be used) provides interesting general information on the mathematical scene as well as continuing exchanges on research problems and papers. There are also occasional contributions from Mabel Mordell. G.208 1927 (re award of Derby Scholarship to assist Davenport at Trinity), 1929 (suggestions for reading and research; Mordell sent his draft papers to the young Davenport for comment). G.209 take up the 'splendid opportunity’ to go to Marburg to work with and Letter of 27 November suggests Davenport should 1930 H. Davenport CSAC 112/3/86 Correspondence 193] Research and publications, mainly on congruences. 1932-33 1934, 1935 1936 (one letter only), 1938, 1939 (one letter only). 1942, 1943, 1944 wet 211 “ale i2ie .214 ‘Zio 1945, 1946 .216 1947 (includes comments on Bibliog. 56), 1948 217 G.H. Hardy. 1949 (not all dated). Some refer to death and obituaries _ ) e G * y G e O e e n B , o G h e M G .218 G sal? G .220 1950 1951 1952 G onl 1953 1954 1955 1956 1957 G 224 1958 1959 G .226 G 222 G 223 G «220 G aah 1960 (one letter only), 1961 (includes draft paper by Mordell 1967 (one letter only), 1968 (one letter only) G.228 ‘On a Pellian Equation Conjecture’, and a 2pp. untitled ms. note by Davenport). 1963, 1964 (includes draft paper by Mordell) G 232 G.229 1962 | G .230 G.231 1965 H. Davenport CSAC 112/3/86 G.233 Muses, C.A. 234 Neugebauer, O. Correspondence Niven, I. O'Baoghaill, M. Triangle of minimum area. Olds, D. Oppenheim, A. 1958 1946-52 Correspondence and research notes, mainly on quadratic forms, also on new University of Malaya, Singapore. Orde; H.4.S. Prime factors of a large number. Ormonde, Marquess of Pedoe, D. Pennington, W.B. 1954-56 Ostrowski, A. 'Schubfachprinzip'. Equations in high numbers, with 2pp. draft reply. Includes 1]pp. draft paper by Pennington 'On Widder's inversion formula’. Phillips, E.G. Littlewood's problem. 1960 1946 1964 Perron, O. Philipp, W. H. Davenport CSAC 112/3/86 Correspondence Pitman, J. 1962, 1965 and n.d. Research, appointments. research notes on 'Cubic Problem’, Theorem of Rado' and 7pp. ms. draft by Davenport on ‘Miss Pitman's simplification’ of Bibliog. 119. 4pp. note by Davenport on 'A Includes material made available by B. J. Birch: G.248-G.251 Polya, G. and Polya, S. 1947-64 Davenport and his wife made the acquaintance of George and Stella Pélya on their Stanford visit 1947-48, and remained lifelong friends. G.248 1947-48 G 249 G.H. Hardy. 1949 Includes letter (7 May) from A.E. Ingham re G.250 decision not to accept permanent post at Stanford. 1950-51 Includes (November 1950) reference to Davenport's G.25]1 1956-64 Various dates, shorter exchanges. Popova, H. 1952 1946-50 1946-68 1947 G.253 G.254 G. 255 1952, 1954 G.253~-G 255 Prasad, A.V. 1955, 1968 (re thesis) Includes draft research papers by Popova and correspondence from A.S. Besicovitch. Prasad was a research student of Davenport in London, working on theory of numbers, before returning to India. Reading in 1954 expresses his gratitude for Davenport's consistent support. Rado was a refugee mathematician in Cambridge in 1933. His letter to Davenport on his appointment to the Chair of Pure Mathematics at Pye, D.R. Rado, R. various dates 1934-68 H. Davenport CSAC 112/3/86 Correspondence Ramanujam, C.P. 1962, 1965 Rankin, R. various dates 1950-63 Redei, L. Hungarian mathematician. 1949, 1953, 1959 Remak, R. Rendle, A.B. Comments on paper. Reuter, G.E.H. Richert, H-E. Ridout, D. n.d. 1954 : 1958, 1959 Robinson, G. de B. 1941 Robinson, R.M. ; G .268 only). .268-G .278 Rogers, C.A. and others 1945-69 1959-60 Includes comments He collaborated with Davenport on several papers 1947-50 Minkowski's results on packing of tetrahedra. by J.W.S. Cassels. Invitation to contribute a book on number theory to new series "Mathematical Expositions’. Rogers was one of Davenport's most distinguished research students at University College, London, where he had been an undergraduate before war service at the Ministry of Supply and where he later held the Astor Chair. on the geometry of numbers, and was first author of the Royal Society Memoir of Davenport. (Giblico 270, 71; 73, 79). G.269 news, sent to Davenport in USA. 1947 1945, appointment as Demonstrator at UCL, 1946 (one letter Frequent reports on research and departmental G.270 1948 Departmental news, research, publications H. Davenport CSAC 112/3/86 Correspondence 1949 G.271 of Markoff, Hurwitz and Segre' and 'Non-homogeneous quadratic forms'. Includes research notes by Rogers 'On theorems G.272 1950 (Bibliog. 81). a 1952, 1953 (Davenport's carbon only), 1954 (research, G.273 appointments, includes note by Davenport for Nature on Rogers's appointment to Chair at Birmingham). G.274 1955 G.275 1956, 1957 G.276 1958 Appointment at UCL. 1964 Includes correspondence with R.F. Wrighton G.277 on packing of spheres, 6pp. note by Davenport on the problem and comments by Rogers. G.278 1965, 1969 G.279, G.280 Rogers, K. 1951-55, 1963, 1964 G.281 Romanoff, N. 1935,. 1937 195] G.282, G.283 Ron, KF. G.280 1954-55, 1963, 1964 various dates 1951-57, 1964-65 G.279 inhomogeneous minima of indefinite Hermitian forms’. Includes research note by Rogers 'The 199, 1900 A research student of Mordell, and later of Davenport, who later worked in USA. Roth was a research student and later a colleague of Davenport at UCL and wrote collaborative papers with him (see Memoir, p.163). 1954, 1956-57, 1964, 1965 G.282 (shortened version prepared by Davenport of a paper by Roth) and French translation by Davenport. Includes 4pp. ms. note 'On certain sets of integers' G .283 H. Davenport CSAC 112/3/86 Correspondence Rumney, M. Sadler, D.H. 1947, 1964 1928, 1940-46 Sadler was a contemporary of Davenport at Cambridge. 1928 congratulates 'Dave' on Yeats prize; correspondence 1940-46 describes wartime work for Admiralty, raids on Bath, visit to Germany and meeting with Hasse 1945, etc. Card of Saelman, B. 1952 Problem in elliptic integrals. Salié, H. Sawyer, D.B. Scherk, P. 1931, 1933 1957, 1961 1951 Theorem on addition of residue classes.. Schinzel, A. 1962, 1966-69 291 ave 1965-69 Schmid, H.L. Schmidt, F.K. 1937 1960 .293, G.294 Schmidt, W.M. Correspondence, mainly on publications (Bibliog. 173, 183, A Polish mathematician and graduate student of Davenport at Cambridge, who collaborated with him on several papers. Schmidt spent part of the academic year 1966-67 in Cambridge and wrote several collaborative papers with Davenport. Various research problems. Ms. drafts by Davenport for work with Schmidt, 4pp. and G .293 185, 188). G.294 20pp. Schnitzer, F. 1952-57 H. Davenport CSAC 112/3/86 Correspondence G.296 Schoenfeld, L. Large sieve problem. G.297 G.298 Schwarz, S. Shovelton, S.T. G.299-G .303 Siegel, C.L. 1947 1956 1938-68 Siegel, a distinguished German mathematician, was born in Berlin. Much of his pre-war academic life was spent in G&ttingen, to which he returned in 195] after residence in USA. G.303, Siegel's account of events in his life and recollections of many leading figures in German mathematics. This appears to have been related to Davenport, and written up by him, in 1966 during his stay in Gdttingen as Gauss Professor (see G.301). Of special interest is 1938, 1939 (letter of 16 July includes suggestion that G.299 Siegel and Davenport should meet in Denmark in March 1940, referred to in the recollections). G.300 1941, 1942 (from Princeton), 1954-57, 1964. 1965-66 G.302 1966-68 Includes See also These are ms. accounts in Davenport's 'Siegel', 5pp. dated At Kneser's', 5pp. dated 27 July 1966. Correspondence and arrangements re Gauss Siegel's recollections. G .303 hand: 'Siegel', 5pp. dated 20 and 22 July 1966; 26 July 1966; ‘Siegel Sierpinski, W. 1959, 1963, 1964 Mainly re publications in Acta Arithmetica, including Bibliog. 149. G.301 Professorship for Davenport at Gittingen, May-July 1966. notices of lectures and draft in German of Bibliog. 171. C.108-C.114. Includes comment by J.W.S. Cassels. Smith, G.S. Research problems and notes, mainly fractions for irrational numbers. 1951 1953, 1955 1959 Smith, C.A.B. Spencer, D.C. H. Davenport CSAC 112/3/86 Correspondence Sprenger, E. Paper on 'Odd numbers', redrafted by Davenport. Sprindzuk, V.G. 1967, 1969 1962 1966-67 nds Srinivasan, B.R. Stark, H. Steen, S.W.P. Research note. Steward, G.C. Translation of a Russian paper by Kotelnikoff. Stoller, G. Waring's problem. Swinnerton-Dyer, H.P.F. 1953-57 1958 1951 Szegt, G. 1948-49, 1956 Szekeres, G. Szele, T. Includes research note on ‘Davenport's theorem’. Correspondence, research notes and problems (not all dated) including collaborative paper (Bibliog. 107). Correspondence 1956 includes letters re symposia at 1958 Congress and a memorandum by S. Bergman on complex variables. Todd, J.A. Titchmarsh, E.C. One letter only. Taussky-Todd, O. 1950, 1957 1957 H. Davenport CSAC 112/3/86 Correspondence G.322 Tschebotareff, G.N. Re recent death of his father. Turan, P. and Turén, V. 1934, 1947, 1964-67 Research and publications, including contributions to memorial volume for E. Landau (Bibliog. 172). Ursell, H.D. Uspensky, J.V. Vallance, L.S. 1969 1947 1955-57 van der Corput, J.G. and van der Corput, J. 1946-48, 1952-53, 1961 Visits, publications, research. Includes a little personal correspondence. van der Pol, B. , 1953 van der Waerden, B.L. 1932-33 G.330 1947-48 G.331 1950-51 1955-56 1949 1947-60 . 329 Vandiver, H.S. .330-G.334 Varnavides, P.L. Comments on draft papers by Davenport. The correspondence is mainly on research and Varnavides was a research student of Davenport at London and subse- quently worked abroad. publications and includes drafts of papers submitted by Varnavides. 1957, 1959-60 Includes various drafts of papers on quadratic forms. G .332 1952-54 G .333 G.334 H. Davenport CSAC 112/3/86 Correspondence G.335, G.336 Walfisz, A. 1930-33, 1936, 1949-57 Pre-war corres pondence is from Radost; post-war correspondence is from Tiflis. G.335 1930, 193] 1932-33 On research and publications by Walfisz and S. Chowla, and including two drafts of paper by Chowla 'On the class- numbers of binary quadratic forms' (in Walfisz's hand) and copy of letter by Walfisz to Chowla. See G.64. 1936 G.336 exchange of reprints. 1949, 1954, 1956-57 Brief correspondence, mainly on Ward, G.W. Contemporary of Davenport at Trinity. G.338-G.344 Watson, G.L. 1950-60 On returning to Britain, he’ | Despite the paucity of letters G .340 1952 Includes research note. G .338 1950 G.339 1951 Includes drafts, etc. for collaborative paper G.341 (Bibliog. 103), and other research notes. 1953 After taking a mathematics degree at Trinity, Cambridge, in 1930, Watson entered the Indian Civil Service. became a mature research student (part-time) of Davenport in London and wrote a collaborative paper with him. from Davenport, the correspondence gives a full account of research, publications and career and includes several draft papers. 1960 1956 (one letter only), 1957 (includes research note), 1958 1954 (one letter only), 1955 (includes drafts for papers and G .343 (includes research note). Includes draft papers, and 5pp. ms. draft for G .344 part of Bibliog. 119. 1959 G .342 research notes). H. Davenport CSAC 112/3/86 G.345 Watson, G.N. 1933, 1945 Correspondence Correspondence 1933, on a problem of Davenport, includes ms. notes for a solution by Watson. Correspondence 1945 is re Davenport's draft obituary of W.E.H. Berwick (Bibliog. 65) and includes ms. suggestions and additions by Watson. Whitehart, F.E. 1950 Elementary proof of the prime number theorem. Whiteley, J.N. c. 1959-60 Research and publications, including draft papers. Few letters dated. Whyte, L.L. 1949, 1952 Correspondence and notes re points on a sphere. Williams, W.L.G. Invitation to Davenport to a Chair at McGill. Wonham, W.M. 1952, 1957 1958 1965 1954-56 Random noise. Wright, E.M. Youngs, J.W.T. Zeeman, E.C. Proposal for National Mathematics Research Centre. Correspondence 1952 is re 3rd edition of 'Hardy and Wright' Introduction to the theory of numbers (published 1954). In alphabetical order. Zulauf, A. Research and publications on prime numbers. Shorter scientific correspondence (not indexed). Zervos, S.P. Mathematical papers of P. Zervos (father of S.P.). 1952 Zygmund, A. Includes note by Davenport in reply to problem. H. Davenport CSAC 112/3/86 Correspondence G.358-G.372 References, appointments, theses, requests for advice 15 folders, in alphabetical order. .358 O o A O O 9 9 @ ® © . 364 9 . 365 'Cranks' (Davenport's description). Some with replies by Davenport, or notes for a reply by colleagues. 1 box. H. Davenport CSAC 112/3/86 BIBLIOGRAPHY Reproduced with permission from Biographical Memoirs of Fellows of the Royal Society, 17, 1971, 187-192. (1) 1931. On the distribution of quadratic residues (mod ). 7. Lond. Math. Soc. 6, 49-54. (2) (3) (4) (5) (6) (7) (8) 1931. On Dirichlet’s L-functions. 7. Lond. Math. Soc. 6, 198-202. 1932. On the distribution of the /th power residues (mod p). 7. Lond. Math. Soc. 7, 117-121. 1932. On a generalization of Euler’s function $(n). 7. Lond. Math. Soc. 7, 290-296. 1933. On certain exponential sums. 7. fiir. Math. 169, 158-176. 1933. On the distribution of quadratic residues (mod p) (second paper). 7. Lond. Math. Soc. 8, 46-52. 1933. Uber numeri abundantes. 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Soc. 24, 271-280. 1950. (With C. A. Rocers.) On the critical determinants of cylinders. Quart. 7. Math. (2), 1, 215-218. 27 (1952) 25125 198. 19-24. 32-41. Harvard, 1, 166-174. C.N.R.S. Paris, 24, 41-43. J. Lond. Math. Soc. 25, 119-125. 1950. Study and research in mathematics. Math. Gaz. 34, 161-165. 1950. Waring’s problem (contribution to the obituary notice of G. H. Hardy). 1950. Euclid’s algorithm in certain quartic fields. Trans. Amer. Math. Soc. 68, 508-532. 1950. Note on a binary quartic form. Quart. J. Math. (2), 1, 253-261. 1950. L’algorithme d’Euclide dans certains corps algébriques. Colloques Internat. du 1950. Sums of three positive cubes. 7. Lond. Math. Soc. 25, 339-343. 1951. Note on a principle of Lipschitz. 7. Lond. Math. Soc. 26, 179-183. 1951. On the class-number of binary cubic forms (I). 7. Lond. Math. Soc. 26, 183-192; 1951. On the class-number of binary cubic forms (II). F. Lond. Math. Soc. 26, 192- 1950. Recent progress in the geometry of numbers. Proc. Internat. 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On the product of n-linear forms. Proc. Camb. Phil. Soc. 49, 190-193. . (With G. L. Watson.) The minimal points of a positive definite quadratic form. Mathematika, 1, 14-17. . Simultaneous Diophantine approximation. Mathematika, 1, 51-72. . On a theorem of Furtwangler. 7. Lond. Math. Soc. 30, 186-195. . Simultaneous Diophantine approximation. Proc. Internat. Congress of Math. Amsterdam, ITI, 9-12. . (With H. P. F. Swinnerton-Dyer.) Products of inhomogeneous linear forms. Proc. Lond. Math. Soc. (3), 5, 474-499. . (With K. F. Rots.) The solubility of certain Diophantine inequalities. Mathematika, 2, 81-96. . (With K. F. Roru.) Rational approximations to algebraic numbers. Mathe- matika, 2, 160-167. . Le recouvrement de l’espace par des sphéres. Colloque sur la théorie des nombres (Centre Belge des Recherches Mathématiques), pp. 139-145. . Note on a theorem of Cassels: Proc. Camb. Phil. Soc. 53, 539-540. . Indefinite quadratic forms in many variables. Mathematika, 3, 81-101. . 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Cubic equations of additive type. Phil. Trans. Royal Soc. Soc. Lond. A, 293, 1-18. Math. Annalen, 169, 118-135. (166) (167) 35, 3-8. 10, 181-185. H. Davenport CSAC 112/3/86 Bibliography . (With H. Hatsersram.) The value of a trigonometrical polynomial at well spaced points. Mathematika, 13, 91-96. . (With D. J. Lewis.) Notes on congruences III. Quart. 7. Math. 17, 339-344. . (With H. Haserstam.) Primes in arithmetic progressions. Michigan Math. 7. 13, 485-489. . Eine Bemerkung iiber Dirichlets L-Funktionen. Géttinger Nachrichten, pp. 203- 212. . (With E. Bomsreri.) On the large sieve method. Abhandlungen aus Zahlentheorie u. Anal. Zur Erinnerung an Edmund Landau (1877-1938). Berlin: VEB Deutsch. Verlag d. Wiss. pp. 11-12. real numbers by quadratic . (With W. M. Scumipr.) Approximation to irrationals. Acta Arithmetica, 13, 169-176. . (With E. Lanpau.) On the representation of positive integers as sums of three cubes of positive rational numbers, Abhandlungenaus Zahlentheorie aus Anal. Zur Verlag d. Erinnerung an Edmund Landau (1877-1938). Berlin: VEB Deutsch. Wiss. pp. 51-53. 1968. Bases for finite fields. 7. Lond. Math. Soc. 43, 21-39. 1967. On a theorem of Heilbronn. Quart. F. of Math. 18, 339-344. 1968. (With W. M. Scumipt.) A theorem on linear forms. Acta Arithmetica, 1967. A. E. Ingham. Nature, Lond. 216, Sit. 1967. (With H. Haserstam.) Corrigendum and addendum. Mathematika, (168) (169) (170) (171) (172) (173) (174) (175) (176) (177) (178) (179) (180) (181) (182) (183) 209-223. 229-232. 14, 14, . Trans. 15, 505. Acta Arithmetica, 15, 393-416. Maths. (Houston), 12, 74-98. Royal Soc. Lond. A, 264, 557-595. Math. (2), 20, 129-137. : (185) (186) (187) (188) Symposia mathematica, 4, Academic Press, pp. 113-132. Mathematica Societatis Fanos Bolyai, 1968. Budapest and Amsterdam, pp. 15-25. (184) 1969. (With D. J. Lewts.) Simultaneous equations of additive type. Phil. (With W. M. Scumrpr.) Dirichlet’s theorem on Diophantine approximation, 1971. (With D. J. Lewts.) Two additive equations. Proceedings of Symposia in Pure 1969. (With A. Baker.) The equations 3x2—2 = y? and 8x2—7 = 22. Quart. 7. 1969. (With W. M. Scummr.) Approximation to real numbers by algebraic integers. 1970. (With W. M. Scumrpr.) Dirichlet’s theorem on Diophantine approximation. alta Mathematica. London: Istituto Nazionale di (With H. Havsersram.) Corrigendum. Michigan Math. 7. 1968. 1970. (With W. M. Scummt.) Supplement to a theorem on linear forms. Colloquia 2. Number Theory. Debrecen, Hungary, 1968. A note on Thue’s theorem. Mathematika, 15, 76-87. 1969. (With E. Bomsrerr.) Some inequalities involving trigonometrical polynomials. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. 23 (Fasc. 2), 223-241. Acta Arithmetica. (In the press.) A determinant of linear forms. Mathematika, 18, 100-104. 1971. 1971. Homogeneous quadratic equations. Mathematika, 18, 1-4. — A combinatorial problem connected with differential equations, II. (Edited (With D. J. Lewss.) Values of positive definite forms in many variables. (With H. Herrsronn.) On the density of discriminants of cubic fields. Bull. (191) 1971. (With H. Hemsronn.) On the density of discriminants of cubic fields, IT. by A. Schinzel.) Acta Arithmetica, 17, 363-372. (189) 1970. (190) 1969. II. Acta Arithmetica, 16, 413-424. (192) 1971. (193) (194) (195) Proc. R. Soc. Lond. A, 322, 405-420. ‘Lond. Math. Soc. 1, 345-348. H. Davenport CSAC 112/3/86 INDEX OF CORRESPONDENTS ADAMS, A. ADAMS, J. F. ADRIAN, Edgar Douglas, Baron AITKEN, Alexander Craig AITKEN, Sir Robert ANKENY, Nesmith C. ANNAN, Noél Gilroy, Baron AP SIMON, H. ARCHBOLD, J. G. W. ARMITAGE, J. Vernon ASHBY, Eric, Baron ATKIN, A. AUSTIN, M. O. C. Ga 136 Acol aes G.2 G.139 G.3 A.70 G.4 A.47 A.76, D.203, G.5-G.7 A.76 G.8 G.9 BAILEY, W. N. BAKER, Alan BAMBAH, RR. P. BERLOWITZ, Bernard BATEMAN, Paul T. BEHREND, Felix A. BARNES, Eric S. BASU, S._ K. BESICOVITCH, Abram Samoilovitch A.57, A.62 A.77, D.196 G.10-G.12 GA3 G.14 D.90, G.15 G.16 G47, G.37 G.24 .19 A.77, D.112-D.116, D.143, D.155, D.210-D.212, G.20, G.92 A.42, A.62, A.77, G.18, G.252 See also B. 57 BLANEY, Hugh BLUNDON, W. BILLING, Gunnar BIRCH, Bryan John BERNDT, Bruce J. G.21-G.22 H. Davenport CSAC 112/3/86 Index of correspondents BOAS; Kos P... dvr. BOHR, Harald BOLLOBAS, Béla BOMBIERI, Enrico BOSANQUET, L. Stephen BOWMAN, Frank BOYS, Samuel Francis (Frank) BRAGG, Sir (William) Lawrence BRANDON, R. W. BRAUER, Alfred BRAUER, Richard BRJUNO, A. OD. BROADBENT, J. Alun A. BROUGHTON, Arthur BROWN, David Spencer BOREL 65. £. BUHL, G. G25 G.26 A71, O27 G.28-G 39 A.57, A.62, G.40, G.152 A.62 G.136 A.70 G.A4l E116, @.42 G.42 G.43 A.62, G.44 A. 77 G 45 G 46 G .47 G .48 BURGESS, David Albert BURKILL, John Charles BURNABY, John BURT, Sir Cyril A. A. A. G. A. BULLEN, Keith Edward BUTLER, Richard Austen, Baron CAPILDEO, R CASSELS, John William Scott owl Liew. ¢. 62, D.203,. F.15, G.52-G.56, 267, Ger 57 58 60 H. CHALK, JohnH. CHAMPERNOWNE, Arthur CHANDRASEKHAR, Lalitha A.47, A.62, A.70, A.78, G.59, G.60 CHAN DRASEKHAR, Subrahmanyan CHASE, R. E. H. Davenport CSAC 112/3/86 Index of correspondents CHATELET, Frangois CHATLAND, Harold CHAUNDY, Theodore William CHOWLA, S. CLEMMOW, P. C. COHEN, Paul Joseph COHN, Harvey Le A; «J. COLLINGWOOD, Sir Edward CONWAY, John H. COOPER, Sir William Mansfield CORCORAN, John P. COULSON, Charles Alfred COURANT, Richard COXETER, Harold Scott MacDonald (Donald) COXETER, Lucy G .62 y a s m o O O O e G e S 0 2 .60, G.63 .66 .64-G .66 136 .67 .78, G.68, G.69 .70 .78, G.71 b.127 .57, A.78 9] .47, A.70 ee A.70, A.78, G.73- 76 ATG e 27 Q DAVIES, Merton DAVIS, Clive S. DELAUNAY, B. DERRY, Douglas DE WITTE, Paul CRIDLAND, Nigel 74 78 79 .80 .81 de BRUIJN, N. G. DAINTON, Frederick Sydney, Baron 70,22. 8, 1G 85 F O O 79 .268 .83 .84, G.85 > : g r a R O S B 0 . 0 O R DOLCIANI, Mary Patricia DUMIR, Vishwa Chander DUFF, Patrick William DIRAC, Gabriel A. Ga A/a? Ore DRAIM, Nick A. DRAZIN, Michael DUBREIL, Paul DIENES, Paul H. Davenport CSAC 112/3/86 Index of correspondents DuVAL, Patrick DYSON, Freeman John A.79, G.87 See also A. 53 G.88 EDDINGTON, Sir Arthur Stanley See B.58 EDKINS, Ci Ww. EQGOLESION, H.-G. EICHLER, M. Beko, Peter'De4 T. A; ENNOLA, Veikko ERDOS, Paul ERRERA, Alfred ESTERMANN, T. EVANS, Benjamin Ifor, Baron A.24, A.39, A 47 A.63 G.89 A.80, G.90 G.9] A.80;.D.91. 6.92 See also D.210 G.93 A.80 See also G.94 G.276 EVELYN, Sir John (Jack) G.95 G. FENNA, Donald FEW, L. FJELLSTEDT, L. FLANDERS, Harley Piette aK FRIEDLANDER, F. FROHLICH, Albrecht GUY, Richard K. GILLIS, J. GODWIN, H. GOODSTEIN, R. GRUNWALD, G. J. H. Davenport CSAC 112/3/86 Index of correspondents HADAMARD, Jacques HALBERSTAM, Heini HALDANE, John Burdon Sanderson HALL, Marshall HALL, Philip HARDY, Godfrey Harold HASELGROVE, C._ B. HASSE, Helmut HAYMAN, Walter Kurt HEAP, A. G.104 A.63, A.70, A.81, D.207, G.34, G.83, G.105 See also A.5 G.106 G.107 A.60, A.70, A.81, G.108, G.136 See also B.71, B.72 A.39, A.42, A.52, G.109- G.114, G.126 See also B.92, C.133, C.134, D.200, G.117, G.217, G.249 S.115 A.81, E.1, E.2,; G.W6-G.122 See also G.114, G 285, G.303 A.63, A.8] A.38 HEILBRONN, Hans Arnold HOFREITER, N. HOLLOND, H. A. HEINHOLD, J. HENSTOCK, Ralph HIRSCH, Kurt A. HLAWKA, Edmund HODGKIN, Sir Alan (Lloyd) HODGE, Sir William (Vallance Douglas) A.57, A.63, A.81, G.68, G.123-G.142 See also D.39, G.110 G.143 G.144 A.63, A.81, G.145 A.81, G.146 G.136, G.147, G.316 A.70 G.148 A.81 G.149 G.150 A.48, A.63 G.15] HOOLEY, Colin HOPF, Heinz HOWARTH, Leslie HUA, Loo-Keng H. Davenport CSAC 112/3/86 INGHAM, Albert Edward Index of correspondents 136 E.129, E.130, G.152, G.153, G.249 INKERI, K. ISRAEL, Neil JAEGER, John JARNIK, V. arreny, ao: B. JEFFREYS, Bertha, Lady JENKINS, G. M. JONES, W. — Burton KANAGASABAPATHY, P. KEMMER, Nicholas KESTELMAN, Hyman KREISEL, G. G.154 G.92 A.82 G.158 A.48, A.56 A.82 G.159 G.84 G.160 G.161 A.82, G.162 G.163 A.82 G.164 G.165 G.166 G.167 LANDAU, Edmund See D.184, D.185 KNAPOWSKI, S. KOBER, Hermann LANDAU, Marianne KHAN, Nisar Ahmed KOSAMBI, D. D. KITSON CLARK, George Sidney Roberts G.174 LEVEQUE, William J. LEDERMANN, Walter LEHMER, Dick H. D.185 G.168 G.169 G.170 G.171 A.82 LANG, Serge LEECH, John (Bill) G.172,.G.173 LEHMER, Emma LEVY, M. Davenport H CSAC 112/3/86 Index of correspondents LEWIS, Donald J. LIGHTHILL, Sir (Michael) James LINFOOT, Edward Hubert LINNIK, Yu.V. LIFLEWOOD, D.. E LITTLEWOOD, John Edensor LOGAN, M. LONDON MATHEMATICAL SOCIETY McANDREW, H. MACBEATH, Alexander Murray McCREA, Sir William Hunter MACK, John MCLEOD, J. ° B. MAHLER, Kurt MORDELL, Louis Joel G.175-G.184 A.82 A.48, A.57 A.82, G.185 G.186 A.41, A.82, E.131, Go187 A.64 A.60, A.90, G.188, G.189 G.190 A.64, G.191 A. 64 G.192 G.193 ASE A644, AGG 194- G.201 G. 202 A.71 G.203 G.204 G.205 A.83 A.48, D.37, G.206 G.38, G.207 MANN, Heinrich B. R. meen, 3 Ge FP, MILNE, Edward Arthur MARTIN, Sir David Christie MENDELSOHN, Nathan S. MONTGOMERY, Hugh Lowell MATTHEWS, K. MAYER, Alfred G.233 A.30, A.50, A.52, A.64, A.83, D.203, E.17, G.123, G.203-G. 232 See also A.3, G.69 MOTT, Sir Nevill Francis MORRELL, A..e: 3a, +H. A. 64 A. 64 G.83 MURDOCH, B._ H. MUSES,.C. =" A, H. Davenport CSAC 112/3/86 Index of correspondents NEUGEBAUER, O. NEUMANN, Bernhard NIVEN, Ivan NYHOLM, Sir Ronald (Sydney) O'BAOGHAILL, Mary OFFORD, A. Cyril OLDS, Douglas OPPENHEIM, Tan Sri Sir Alexander weet. Aas, ORMONDE, James Arthur Norman Butler, 6th Marquess of OSTROWSKI, A. G.236 A.49, A.64, A.83 G.237 G.238 G.239 G.240 G.241 PAGE, Arthur PEDOE, D. PENNINGTON, W. B. POLYA, George PHILLIPS, Edgar G. PITMAN, Jane PARS, Leonard Alan PEARSON, Egon PERRON, Oskar PHILIPP, Walter POLKINGHORNE, John Charlton A.57 A.39, A.84 A.7] G.242 A.65,’A.71, 6.249 G.244 G.245 A.65, G.246 A.84, G.247 A.84 A.54, A.56, G.256 D.92, G.248-G.25]1 See also D.55 D.92, G.248-G.251 G.252 G .253-G.255 POLYA, Stella POPOVA, Helen PRASAD, A. — Vindhyachal PYE, Sir David (Randall) H. Davenport CSAC 112/3/86 Index of correspondents RADO, Peter RADO, Richard RAMANUJAM, CC. P. RANKIN, Robert A. REDDER 1. REMAK, Robert RENDLE, A. RENYI, Alfred B RclHERy G, --€..,.¢H:; RICCI, Giovanni RICHERT, Hans-Egon RIDOUT, D. ROBERTS, Donald ROBINSON, G. de B. ROBINSON, Raphael M. ROBSON, R. A.74 A.49, A.65, A.71, A.85, G.257 G.258 A.65, G.259 G .260 G.261 G.262 A.80 G.263 G.28 G.264 R.t3e, Gr265 A.65 G .266 D.164, G.267 A.85 ROGERS, Claude Ambrose ROSEN, David ROTH, Klaus Friedrich ROUGHTON, Francis John Worsley ROYAL SOCIETY RUMNEY, Max ROGERS, Kenneth ROMANOFF, N. A.85, D.41, D.207, D.210- D.212, E.133, G.268-G.278 See also A.3, A.4, C.167, D.81, G.57 G.279, G.280 G.28] A.85 G.282, G.283 A.49 A.68, D.201 G.284 A.71 G .287 SADLER, Cyril SADLER, Donald H. SAELMAN, B. A.49 A.86, G.285 G .286 RUSHTON, William Albert Hugh SALIE, Hans H. Davenport CSAC 112/3/86 Index of correspondents SAMET, Paul SAWYER, Desmond B. SCHERK, Peter SCHINZEL, Andrzej SCID, He cok. SCMMIDT Fa EK. SCHMIDT, Wolfgang M. SCHNEIDER, Theodor SCHNITZER, Franz J. SCHOENFELD, Lowell SCHWARZ, Stefan SEMPLE,. 3.5: ee SHAW, Frank SHOVELTON, Sydney Taverner SIEGEL, Carl Ludwig A.66 G .288 G.289 A.86, D.164, G.290 G.277) G.292 A.85 A.86 A.86, G.295 G .296 See also D.90 G.297 - 66 +66, G.305 A.57, A.66 A A G A S$ A.86, G.304 A A G . 307 G.308 G.309 G.310 G.311 A A G A - 66 “60: A466, G88, GABP: 254, G.298 -06; C3106; Gl 276; .303 . 299% G. R. C. SIERPINSKI, Waclaw SMITH, Cedric A.B. SRINIVASAN, BB. STARK, Harold SMITHIES, Frank SPEER, Dea Ca Seca, S. STEWARD, G. | We SPRENGER, E. SPRINDZUK, V. G.318 A.66, A.86, D.99, E.134, G.315 A G .66, G.136, G.312 66, G.313 .314 49, A.53, A.55 .60, D.92, G.316 ‘B17 SWINNERTON-DYER, Sir (Henry) Peter (Francis) STOPFORD, John Sebastian Bach, Baron SZEGO, Gabor SZEKERES, G, STOLLER, Gerald SZELE, Tibor H. Davenport CSAC 112/3/86 Index of correspondents Taro, d..): 6. TAUNT, Derek TAUSSKY-TODD, Olga TEMPLE, George THOMSON, Sir Joseph John TITCHMARSH, Edward Charles TITCHMARSH, Kathleen TODD, John Arthur TSCHEBOTAREFF, G. TURAN, Paul TURAN, Vera N. URSELL, Harold D. USPENSKY, J. V. A.66 C.52, G.136 A.49, A.66, G.319 A.66, A.87, G.188 A.A] G.152, G.320 A.71 A68 sA BPG. 136°C 21 G .322 G.323 G.323 , VANDIVER, H. _ S. VAELANCE;-L.% S, VARNAVIDES, P. L. VAN DER WAERDEN, B. L. VAN DER POL, Balthazar VAN DER CORPUT, Jeannet VAN DER CORPUT, Jan G. G.326 D.92, G.327 G .327 G .328 G .328A G .329 A.87, D.60, G.330-G.334 A.88, G.338-G.344 © 830, 890 See also G. 64 D.92 a2 [557 A.53 WARD, G. W. WARD, J. Di25 WALD, A. WALFISZ, Arnold WALMSLEY, Charles WATSON, George L. H. Davenport CSAC 112/3/86 Index of correspondents WATSON, George Neville WHITEHART, Fe. E. WirecLeY, J. Wey £3. WIGGLESWORTH, Laurence WILCOCK, Bruce WILLIAMS, W. Lloyd G. WINSTANLEY, Denys A. WONHAM, W. M. Wee al. 3 Le WRIGHT, Edward Maitland WRIGHTON, R._ F. YOUNGS, 2.2. W% O O a 4 347 r a P 88 . 88 O e e 349 33 ) a .350 . 88 .66, A,88; a3! aad. n O ZEEMAN, Erik Christopher ZERVOS, Spiros P. ZULAUF, Achim ZYGMUND, Antoni

# DAVENPORT, Harold v2

Published: 16 January, 2024 Author: admin