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 Deposited in the Library of Trinity College, Cambridge 1986 All rights reserved H. Davenport CSAC 112/3/86 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 Institution of Mechanical Engineers The Nuffield Foundation The Rhodes Trustees The Royal Society of London 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 Items GENERAL INTRODUCTION SECTION A BIOGRAPHICAL AND PERSONAL A.1 - A.137 SECTION B SCHOOL AND UNIVERSITY NOTEBOOKS AND LECTURE NOTES B.1 -B.92 SECTION C LECTURES AND ADDRESSES C.1 -C.193 SECTION D PUBLICATIONS D.1 - D.213 Introduction to Section D SECTION E RESEARCH NOTES AND DRAFTS E.1 -E.135 SECTION F FACULTY OF MATHEMATICS, CAMBRIDGE F.1-F.17 SECTION G CORRESPO NDENCE G.1 - G.373 Introduction to Section G BIBLIOGRAPHY INDEX OF CORRESPONDENTS 21 31 55 78 92 95 125 13] H. Davenport CSAC 112/3/86 GENERAL INTRODUCTION PROVE NANCE 4 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, wherehis gifts for mathe- matics and chemistry were early recognised. At the age of sixteen he was awarded scholarships to attend Manchester University (1924 - 27) winningfirst-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 eventof 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 His first university post was a return to Manchester learn the language thoroughly. as Assistant Lecturer (1937 - 41) and in 1941 he was appointedto his first Chair at In 1945 Davenport, who had married University College of North Wales, Bangor. Anne Lofthouse in 1944, moved to University College London as Astor Professor. first American visit, to Stanford in 1947 - 48, occurred during the London period and was followed by many later transatlantic journeys of varying duration. from the Mathematics Department of University College that Davenport launched the His It was also new journal Mathematika (1953). In 1958 he was elected Rouse Ball Professor of Mathe- 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 Less fully represented are his extensive travels for visits and conferences and work. (which can sometimes only be deduced from a jotted heading on a lecture script) and His contributions to his subject, as his work for the London Mathematical Society. H. Davenport CSAC 112/3/86 5 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.31). 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 material. Ona less technical note is the address given in 1947 at Accrington Grammar School, Davenport's old school (C.131). Conversely, a new generation in the filiation of mathematics is represented by the notes on Davenport's lectures at London in 1946 made by C.A. Rogers, his research student, collaborator and eventual successor in 1958 as Astor Professor (C.167). Section D (Publications) includes drafts, sometimes accompanied by correspondence with collaborators (see especially D.110-D.120) or publishers, for Davenport's many papers. These have been linked wherever possible to the numbered list in the Bibliography appended to the Royal Society Memoir by C.A. Rogers and others (Biographical Memoirs of Fellows of the Royal Society, 17, 1971); a copy of the Bibliography is reproduced with permission on pp. 125-130. In addition, there is considerable material relating to work not listed in the official bibliography; this includes Davenport's books on The higher arithmetic (D.89 - 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 6 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. Of 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 can be traced. Early correspondence with E.A. Milne (G.206) and L.J. Mordell (G.208) show their recognition and fostering of Davenport's talent, and that with E. Bombieri (G.28 - G.39), D.J. Lewis (G.175 - G.184) and C.A. Rogers (G.268 - G.278), among many others, indicate his continuing contributions. Special mention must be made of Davenport's close connection with German 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 pondence with H.A. Heilbronn (G.123 - G.142), H. Kober (G.165), K. Mahler (G.194 - 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 language is evident both in the corres pondence and in the drafts for lectures and papers elsewhere in the collection. H. Davenport CSAC 112/3/86 ACKNOWLEDGEMENTS 7 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 Jeannine Alton Peter Harper Margaret Erskine H. Davenport CSAC 112/3/86 Biographical and personal A.7 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. A.8-A.14 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 made by Mrs. Davenport of her husband's accountofhis early life to 1929, with reference to his childhood, family back- ground and his undergraduate days at Manchester. Typescript of Davenport's comments on his own published papers, 1-120 (see Bibliography), dictated to his wife and D.J. Lewis, 1969. App. miscellaneous ms. autobiographical notes, n.d. 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. prompted by visit toa conference there, September 1966. A.8 A.9 A.10 A.11 A.12 A.13 H. Davenport CSAC 112/3/86 Biographical and personal 10 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.16 December 1919-April 1921 A.18 March 1923-July 1924 Two letters from Lancashire Education Committee, 1920, re "Open Junior Exhibitions', one of which was awarded to Davenport. A.20-A.23 Educational certificates, 1922-24, issued by Joint Matriculation Board. A.20 Examination, July 1922'. "List of Successful Candidates, School Certificate A.21 School Certificate, July 1922. A.22 Matriculation Certificate, July 1922. A.23 Higher School Certificate, July 1924. (See A.27 for questions papers. ) H. Davenport CSAC 112/3/86 Biographical and personal A.24 Letters from headmaster, 1924, 1927. 11 Letter from old school friend, signed Bottomley, 1934. A.25 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 A.26 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. Higher School Certificate Examination, July 1924. See also A.23. A.28 Honours School of Mathematics, Part I, May 1925. 'Christmas Terminal Examinations', December 1925. A.29 Honours School of Mathematics, Part Il, May 1926. A.30, A.3]1 Two examination scripts written by Davenport for the Honours School of Mathematics, Part II], May 1927, set, marked and preserved by L.J. Mordell, who sent them to Mrs. Davenport in 1971. Covering note (A.30), gives names of other examiners, Bailey, Milne and Chapman, which papers they set and Davenport's marks for each. A.32 Degree Day programme, July 1927. See also A.134, A.135. H. Davenport CSAC 112/3/86 12 Biographical and personal TRINITY COLLEGE, CAMBRIDGE, 1927-36 A.33 A. 34 A.35 A.36 A.37 A.38 A.39 A.40 A.4l 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 andthe Walker Prize (1929). Letter from the Victoria University of Manchester, July 1927, re scholarship and other arrangements. Trinity College classlists, 1928; inter-college examination paper, n.d.; ms. note of 'May Marks'; battels bill for Michaelmas Term, 1929. '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. Three letters of congratulation, 1929 and n.d., on Cambridge successes, including two from former mathematics mistress, A. Heap (see Memoir, p. 159). Telegram announcing election to fellowship at Trinity, 1932; letters and telegrams of congratulation. M.A. certificate, Cambridge, 1933. Note from J.J. Thomson, 1936, re weekend visit to 'Christ-Church', asking Davenport 'to represent the College’. Also included are two notes re mathematical problems from J.E. Littlewood, n.d. (see Memoir, p.160). H. Davenport CSAC 112/3/86 Biographical and personal 13 A.42 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). A.43 ‘Conditions of Appointment’ for post of assistant lecturer, 1937. Announcement of appointment, n.d. (press-cutting only). A.44 A.45 Sc.D.. certificate, Cambridge, 1938. Letter of application for Chair of Mathematics, University of Durham, 1939, with bibliography. A.46-A.49 Fellowship of Royal Society, 1940. A.46 Receipts from Royal Society for fees. A.47-A.49 Letters of congratulation. A.47 A-G A.48 H-N A.49 O-T, and first names only H. Davenport CSAC 112/3/86 A.50 A.5] Biographical and personal 14 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 A.52 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. ‘Memorandum! re terms of engagement. Folder includes 1941 bibliography found with this application. Correspondence from Principal, U.C.N.W., re appointment, July, September 1941. Four letters of congratulation. 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’ . Three letters from Vice-Chancellor, University of Manchester, November 1944-February 1945, re possibility of Davenport's succeeding L J. Mordell as Fielden Professor of Pure Mathematics. — A.53 A. 54 A.55 H. Davenport CSAC 112/3/86 A.56 A.57 A.58 A.59 A.60 15 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 Davenportto 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 See A.56, A.57 for correspondence re appointment and congratulatory letters. 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 Letter accompanying cheque for Berwick Prize of the London Mathematical Society, 1954. Letter inviting Davenport to accept Presidency of the London Mathe- matical Society, 1957. H. Davenport CSAC 112/3/86 Biographical and personal 16 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 L-O A.67 5pp. ms. of speech given by Davenportat 'Presentation' to him, 18 June 1958, at University College, London. THE ROYAL SOCIETY'S SYLVESTER MEDAL, 1967 A.68 A.69 Letters from Royal Society informing Davenport of the award, inviting him to attend Anniversary Meeting to receive medal and to Anniversary Dinner, November 1967; invitation cards. Menu and seating plan of 1967 Anniversary Dinner. A.70-A.72 Letters of congratulation: A.70 A-#H A.72 First names and unidentified A.71 M-T A.73 Letter inviting Davenports to Midsummer Banquet of Lord Mayor of London, 1968. H. Davenport CSAC 112/3/86 A.74, A.75 Honorary D.Se., Nottingham, 1968. Biographical and personal 17 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.) A.76-A.89 Letters of condolence: A.76 A.77 A.78 A.79 A.80 A.81 A.82 =A BB C —D E-G H J-L A.83 A.84 A.85 A.86 A.87 A.88 A.89 M,O P Q,R S T,V W Unidentified A.90 Material re Memorial Service, Trinity College, and London Mathe- matical Society Memorial Meeting. A.9] Scrapbook, containing almost exclusively newspaper cuttings re The cuttings include some non- Davenport's career, 1924-1969. mathematical items, such as reports on Accrington Grammar School prize-giving ceremonies. Some loose items. H. Davenport CSAC 112/3/86 18 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 A.102 A.103 A.104 A.105 A.110 A.111 A.112 A.113 A.114 A.120 A.121 A.122 A.123 A.124 1924 1924-25 1925-26 1932-33 1933-34 1934-35 1942 1943 1944 1945 1951 1952 1953 1953-54 1954-55 1960-61 1961-62 1962-63 1963-64 1964-65 A.95 A.96 1927-28 1928-29 A.100 1935-36 A.101 1939 A.106 1945-46 A.107 1946-47 A.108 A.109 1949 1950 A.115 1955-56 A.116 1956-57 A.117 1957-58 A.118 1958-59 A.119 1959-60 A.125 1965-66 A.126 1966-67 A.127 1967-68 A.128 1968-69 A.129 1968-69 H. Davenport CSAC 112/3/86 19 Biographical and personal MISCELLANEOUS ITEMS A.130 2pp. typescript note of German andItalian 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. Szeg8 and H. Heilbronn, gives names, subject speciality, former Davenport states that all were anti- posts and present whereabouts. 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. A 1ol Letter from Secretary of English Speaking Union, 1958, thanking Davenport for suggesting possible members of a selection committee. Letter from Union Mathématique Internationale, 1964, asking Davenport to serve on committee to choose candidates for Fields medals in 1966. A. 132 Postcards sent by friends and colleagues living or visiting abroad, 1948-69. Not indexed. H. Davenport CSAC 112/3/86 20 Biographical and personal A.133-A. 137 PHOTOGRAPHS A.133 Photographs of Davenport, 1911-1968. Oneprint (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 A. 136 Miscellaneous group photographs, all including Davenport. Includes one print of Davenport, P. Erdés and L.J. Mordell (n.d.), one of 'Professor Mordell's Seminar’ (1938) and one of Davenport, Besicovitch and Littlewood (1967). A.137 International Congress of Mathematicians, Harvard conference, 1950. Group photograph. H. Davenport CSAC 112/3/86 21 SECTION B SCHOOL AND UNIVERSITY NOTEBOOKS AND LECTURE NOTES :B.T -B.92 B.1 -B.22 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 B.1-B.22 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. 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. For Davenport's school reports 1919-1924 see A.15-A.18. B.1 B.2 B.3 B.4 B.5 B.6 B.7 B.8 'Chemistry', dated 14 September 1920. "Physics Notebook', dated 14 September. ‘Practical Chemistry', dated September 1922. "Practical Physics', dated September 1922. "Inorganic Chemistry [1J', dated September 1922. "Inorganic Chemistry £21', dated February 1923. 'Physics C1 J', dated September 1922. 'Physics [2J', dated March 1923. H. Davenport CSAC 112/3/86 B.9 B.10 School and university notebooks and lecture notes 22 '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. 'Hydrostatics &c.', n.d. ‘Chemistry Notes', n.d. B.20 'Mathematics', n.d. B.21 B.22 Davenport's Accrington address (inside front cover) replaced by address in Manchester. Untitled notebook, n.d., containing mathematical problems. 'Extracts from various writers', n.d. Two loose enclosures: ms. drafts of speeches 'Should Capital Punish- ment be Abolished?' and re question 'whether Science or Art contributes the more to civilisation’. H. Davenport CSAC 112/3/86 School and universitynotebooks and lecture notes 23 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). B.23 B.24 B.25 B.26 B.27 B.28 B.29 ‘Mathematics IVa'. "Mathematics IVb'. Note on inside front cover: 'Ist year BSc Hons. Maths Notes’. ‘Maths. Va'. ‘Maths. Vb’. ‘Maths. Vb (continued)'. "Applied Mathematics B'. ‘Applied Maths. D'. Note on inside front cover: 'Second year BSc. Honours Maths notes'. B.30 ‘Applied Maths D (cont'd)'. H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes 24 B.31-B.54 LECTURE AND CLASS NOTES These are loose ms. pages of notes on the literature, notes on lecture courses and class work and exercises by Davenport. Many bear an indication of the course number, or of the person giving the lectures and/or supervising the work. The material was kept 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 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.3] 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. B.33 1926-May 1927. Ms. notes, all headed 'Maths VI b', all dated October B.34 Transformations. Duporeq Chap. VI' and 'Quadrics'. 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). B.36, B.37 ‘Summarised notes real var. & exs. Via 1926-7’. Contents of a folder so inscribed. B.36 some dated 1927, Ms. notes, variously titled, chiefly on integrals and series, B.37 May 1927. Ms. notes, all headed 'Maths Vla', all dated October 1926- H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes 25 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 (iwo hands); work of 31 January 1927 includes separate page of comments. B.44, B.45 "Hydrodynamics &elasticity 1926-7'. Contents of a folder so inscribed. B.44 Ms. notes, on strain and wave motion. Ms. notes, on potential theory and ellipsoids, with B.45 sequence of notes labelled 'Applied Maths E', dated October 1926- April 1927; several pages marked by tutor, with occasional comment. B.46, B.47 ‘Differential geometry 1926-7'. Contents of a folder so inscribed. 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’. Contents of a folder so inscribed. B.48 "Complex numbers’. Extensive sequence of notes, variously sub-titled, including B.49 Sequence of notes entitled 'Complex Integration’. H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes 26 B.50, B.51 ‘Real variable notes 1926-7'. Contents of a folder so inscribed. Extensive sequence of notes, headed ‘Mathematics Vla', B.50 variously sub-titled, including 'Infinite Series' and 'Uniform Con- vergence of Infinite Products’. B.5] "Fourier Series' and 'Double Integrals’. Three sequences of notes: ‘Integrals with q parameters’, pa B.52, B.53 ‘Differential eqns. 1927'. Contents of a folder so inscribed. B.52 "Elliptic Functions’. Two sequencesof notes: 'Differ ential Equations’ and Extensive sequence of notes entitled: 'Differential Equations’, B.53 variously sub-titled, including 'Properties of Legendre's Polynomials’ and ‘Solution of eqns. by definite integrals’. B.54 Davenport's original folders from B.31-B.53. H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes 27 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 B.56 B.57 B.58 B.59 B.60 B.6] B.62 'Mr. Pollard Systems of orthogonal functions. 1927-8'. Aggregates and functions. 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 1927-8. Almost periodic functions’. sets. Measurability and the theory of measurable A.S. Besicovitch was Davenport's Director of Studies for pure mathematics. See Memoir, pp. 159-60. ‘Combination of observations. Prof. Eddington Michaelmas Term 1928'. 'Fourier's series and other representations of functions Michaelmas Term 1928'. Prof. Hobson. ‘General Dynamics Mr. Pars. Jesus. Michaelmas Term 1928'. 'Mr. Steen. Classical Theory of Numbers. Lent Term 1928’. "Binary forms. Dr. A. Young 1928-29". 18pp. misc. ms. notes enclosed. B.63, B.64 Two untitled notebooks, n.d., probably from Davenport's period as undergraduate in Cambridge. H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes 28 B.65-B.92 LECTURE NOTES, ETC. These are loose ms. pages of notes, chiefly of lectures attended by Davenport. Usually they bear the nameof 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. B.65, B.66 'Mr. Pars. Dynamics’. Contents of a folder so inscribed. Extensive sequence of ms. notes headed 'General Dynamics. Mr. Pars. Michaelmas Term 1928'. B.67-B.70 'Mr. Richmond. Curves & surfaces’. Contents of a folder so inscribed. ‘Algebraic Geometry. Mr. Richmond. Michaelmas Term B.67 1928". Extensive sequence of ms. notes, variously sub-titled. B.68 Lent Term 1929'. 'Curves and surfaces of orders 3 and 4. Mr. Richmond. Extensive sequence of ms. notes, variously sub-titled. B.69 'Kummer's quartic surface’. 12pp. ms. notes. Set of ms. notes (not in Davenport's hand) mostly headed B.70 'Kummer's Surface', some also headed 'Richmond', and dates 7-12 March 1929. H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes 29 B.71, B.72 '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’. B.71 B.72 pp.1-45. 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. B.75-B.77 'A.S. Ramsey. Electricity’. Contents of a folder so inscribed. B.75 Miscellaneous ms. notes, sometitled. B.76, B.77 Extensive sequence of ms. notes headed 'Solenoids' . B.78, B.79 ‘Ramsey, F.P. Foundations of mathematics’ . Contents of a folder so inscribed. B.78 'Other views on the Foundations of Mathematics’. Extensive ms. notes headed 'Kinds of definitions’ and B.79 2 February 1928. 13pp. miscellaneous notes and calculations, 1 page dated B.80-B .84 ‘Lattice points (Steen)'. Contents of a folder so inscribed. 'Cam. undergrad. 27-29'. Pencilled note on folder reads: B.80 ‘Chapter II'. Extensive sequence of notes, headed 'Chapter |’ and B.8] B.82 B.83 B.84 5pp. ms. notes and calculations. Ms. notes and calculations, paginated 22-39. Ms. notes and calculations, paginated 45-77. 8pp. ms. notes and calculations. Sequence of notes, headed 'ChapterIII". H. Davenport CSAC 112/3/86 School and university notebooks and lecture notes 30 B.85-B .87 "Series SS ; 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. B.88 "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’. Sequence of ms. notes and calculations, variously sub-titled . B.89 Davenport's original folders from B.65-B.88. B.90-B .92 B.90, B.91 Lecture notes made by Davenport at Cambridge after taking his B.A. degree. Two series of lecture notes, found together with note 'Notes of lectures attended at Cambridge’: B.90 'Summable series’. B.91 'Inequalities' . B.92 "Hardy Fourier series' 1932. 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' and 'Lebesgue Integral’. H. Davenport CSAC 112/3/86 31 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 C.130-C.158 SOCIETIES, CONFERENCES,etc. C.159-C.193 MISCELLANEOUS AND UNDATED LECTURES C.1-C.4 CAMBRIDGE, 1930s Not dated, but probably 1933-37 during Davenport's period as research fellow at Trinity College. C1, c3 "Algeb. Functions' Contents of a folder so inscribed, n.d. 6.1 algebraic functions. Extensive paginated ms. draft of a series of lectures on C.2 a continuation of C.1. Extensive paginated ms. draft of a series of lectures, probably Folder includes 3pp. paginated ms. notes and calculations, and label from original folder. C.3 C.4 '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 labelled 'Algebra'. H. Davenport CSAC 112/3/86 Lectures and addresses 32 C.5-C.12 MANCHESTER, 1937-41 The only lecture and teaching material surviving from this period was found in an envelope labelled 'Notes Maths VII] 1940-41'. C:5 C.6 Duplicated examination paper 'Pure mathematics VIII', December 1940; ms. draft, including solutions to problemsset. 9pp. ms. draft headed 'VIII Linear Differential equations' related to the above. 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’. C.7 'D. equations of first order but not first degree’, n.d. 6pp. draft of a lecture. C.8 ‘Infinite series’. Ms. draft of course of lectures. C.9 ‘Functions of two variables’. Ms. draft of a lecture. C.10 "Notes on exs.' Ms. draft, probably for a lecture, giving solutions to various problems and examples. C.11 "Fourier series’. Ms. draft of a lecture. C 12 "Solutions in series’ 5pp. ms .draft, probably of a lecture. llpp. miscellaneous ms. drafts, variously titled. H. Davenport CSAC 112/3/86 33 Lectures and addresses C.13-C.16 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. C.13 "Fourier series’. Ms. draft of a series of lectures, originally from a folder labelled "Bangor'. C.14 "Differential equations’. Ms. draft of a series of lectures. Cal5 ‘Differential geometry’. Ms. draft of a series of lectures. C.16 "Infinite series and integrals’. Ms. draft of a series of lectures. C.17-C.51 UNIVERSITY COLLEGE, LONDON, 1945-58 This material was probably all intended for teaching undergraduates, and many lecture drafts are accompanied by reading lists and in some cases bylists of students’ names. There are not only finished drafts, both manuscript and typescript, but also notes and calculations. Only C.17-C.34 can be dated exactly. C.17 Ip. ms. list of topics, probably for a course of lectures, dated 1945-46. "Ideas for the future’, n.d. Ip. ms. list of topics, probably for lectures. H. Davenport CSAC 112/3/86 Lectures and addresses 34 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. C.19 4 topics, variously titled. C.20 term' lecture course. 6 topics, variously titled, with Ip. ms. notes for ‘Summer C.2] ‘First Year Special Analysis’. 6pp. ms. draft of an introductory lecture to first year undergraduates, found with C.18-C.20. C.22, C.23 'The geometry of numbers', 21948 C.22 Ms. draft for a course of lectures. C.23 Rough notes and calculations. C.24 '3rd yr Theory of Numbers. 1952-53. 2pp. ms. outline of a lecture course, giving dates of lectures, with 2pp. ms. notes and calculations. Supplementary to "Higher Arithmetic"', ‘Quadratic forms (supplementary to "Higher Arithmetic")'. 2pp. ms. notes and calculations. 'Theory of Numbers’. Ip. ms. list of students' names and addresses. C.25, C.26 'Classical achievements in pure mathematics', ?1952. Extensive typescript and ms. draft of course of 5 lectures. C.25 1-3. Ip. ms. list of the lectures; introductory remarks and lectures C.26 Lectures 4 and 5. Folder also includes 'The fundamental theorem of algebra’, given to the Bangor Mathematical Society, 4 December 1952. H. Davenport CSAC 112/3/86 Lectures and addresses 35 C.27-C.29 'Various topics in the theory of numbers', 1953-54. 94pp. paginated typescript draft of a course of lectures. C.27 pp.1-41 C.28 pp.42-79 c.27 pp.80-94, and 5pp. diagrams. C.30 ‘Remarks to S 1 class', 1955. 5pp. ms. notes of introductory talk to undergraduate class. C.31-C. 34 "Introduction to the analytic theory of numbers', 1956-57. C.31, C.32 Ms. draft, paginated [C1 1-66, of a course of lectures. 2 folders. C.33 Ms. draft, paginated 83-133. C.34 lecture course; 5pp. ms. notes. 2pp lists of signatures, probably of those attending the C.35 'Theory of numbers (Third year course)’, n.d. App. ms. draft, probably offirst lecture of a course. C.36-C.40 'The geometry of numbers', n.d. Contents of a folder inscribed 'G of N (UCL)’. C.36, C.37 Duplicated typescript with a few ms. corrections. 2 folders. C.38, C.39 Another copy. C.40 2pp. list of topics headed 'Geometry of numbers’ . Ip. ms. note of 'Further topics’. H. Davenport CSAC 112/3/86 C.41-C.51 Lectures and addresses 36 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.4] 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. readinglist. 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. ‘Examples on number theory’. 6pp. ms. problems andsolutions. 'Theory of numbers. Literature’. Ip. ms. reading list. '5. Gauss's Sum’. C.46 8pp. ms. draft of a lecture, probably one of a series. ‘Higher power residues’ . App. ms. draft, probably unfinished, of a lecture. Ip. ms. notes outlining a course of lectures. C.47. Quadratic residues’ . —'Il_ Divisibility and the primes', ‘Ill Congruences', 'IV 3pp. ms. outlines of lectures. '5 (k/P) as a function of P'. 2pp. ms. draft. H. Davenport CSAC 112/3/86 37 Lectures and addresses C.48 '2. Gauss's lemma'. 2pp. ms. draft. '3. The law of quadratic reciprocity’. Spp. ms. draft. '4. An algorithm for ():. 2pp. 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 C.51 Inside cover of original binder, with ms. calculations. H. Davenport CSAC 112/3/86 Lectures and addresses 38 C.52-C.97 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. C.52-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. list of dates of lectures and topics to be covered. colleague for loan of notes. Includes letter of thanks, 1960, from (C.52). 2 folders. C.54 'The Gamma Function’. Miscellaneous shorter notes and drafts. C.55-C.59 'Diophantine Approximation', 1961-62. 78pp. ms. draft of course of lectures. C.55 includes C.55-C.57 App. outlines of topics to be covered, Ip. list of students' names and 3pp. preliminary draft and notes. 3 folders. C.58 Shorter notes and calculations. C.59 the course, on Cassels's theorem. 10pp. draft, possibly of an optional lecture for the end of Folder includes reprint of Bibliog. 111. C.60-C.62 'Functions of a complex variable (Easter term, 1962)'. C.60, C.61 46pp. ms. draft for course of lectures. 2 folders. C.62 'Problems'; ‘Solutions’. Includes original folder, inscribed with calculations. H. Davenport CSAC 112/3/86 Lectures and addresses oo C.63-C. 66 'Theory of numbers (Introductory Part III)', ?1963. C.63-C.65 C.65 includes Ip. ms. reading list. 83pp. ms. draft for lecture series, 1p. dated 1963. 3 folders. C.66 Ilpp. ms. draft; miscellaneous ms. notes and calculations. C.67 'Two problems of Mordell', 1964. 10pp. ms. draft of a seminar paper, given 25 February 1964. C.68-C.72 'The geometry of numbers (Lent Term, 1964)'. C.68-C.70 103pp. ms. draft for lecture course. 3 folders. C.7] Miscellaneous shorter notes and drafts on topics to be covered. C.72 9pp. ms. notes and calculations. Also included here are Ip. ms. notes in an unidentified hand and reprints by K. Mahler. C.73-C.75 'Diophantine approximation (Michaelmas term, 1964-5)’. C.73, C.74 Ip. list of pupils, October-December 1964. 7lpp. ms. draft for lecture course. 2 folders. C.73 includes C.75 Miscellaneous ms. notes and calculations. C.76, C.77 'Theory of numbers (Part I], Optional)', 1964-65. C.76 6pp. ms. draft for lecture. Ip. typescript outline of lecture course, dated October 1964, with Ip. ms. list of topics to be covered in each lecture. C.77 5pp. ms. of questions, problems and examples. 2pp. typescript entitled ‘Theory of numbers (Part II), 1964-65 Problems’ . 2pp. typescript entitled 'Theory of numbers (Part Il), 1964-5 Outline Solutions’. H. Davenport CSAC 112/3/86 Lectures and addresses 40 C.78 'The basic inequality of the large sieve method', 1 November 1966. 10pp. ms. draft for seminar paper. C.79 'Dirichlet's L-functions. (Michaelmas term 1966-7)’. 2lpp. draft for lecture, with Ip. ms. calculations. C.80-C.85 "Additive number theory', ?1967-68. C.80-C.82 119pp. ms. draft for lecture course. 3 folders. C.83 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. C.85 "Mordell's finite basis theorem’. 6pp. ms. draft for lecture, with 3pp. ms. notes and calculations. C.86-C.88 "Cambridge Lectures (additive)', n.d. 60pp. ms. draft for course of 3 lectures from folder labelled as above. C.86 'Waring's problem’. The first page of this lecture was used as the cover illustration of the 5th edition of Davenport's The Higher Arithmetic (1982), although the text does not appear elsewhere in the book. C.87 'The Hardy-Littlewood method’ . C.88 'The Asymptotic formula: Vinogradov’. Includes 5pp. alternative version. C.89-C.91 'The distribution of the primes’, n.d. 95pp. ms. draft for course of lectures. 3 folders. H. Davenport CSAC 112/3/86 C.92-€:95 "The Riemann Zeta-function', n.d. Lectures and addresses 4] C.92 "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. C.96 "References for equations in many variables’, n.d. 3pp. ms. list, possibly to accompany a course of lectures. C.97 "Davenport: Theory of Numbers', n.d. Two typescript drafts, 3pp. and 2pp., oflist of problems. ‘Davenport: Geometry of Numbers', n.d. Two typescript drafts, 3pp. and 2pp., of list of problems. C.98-C.129 LECTURES ABROAD Davenport made manyvisits abroad (see Mrs. Davenport's biographical notesat A.7). The material here is from three universities with which he had particularly close connections: Stanford, G&ttingen and Michigan. up toa full academic year, and could involve teaching and examining as well as lecturing. Visits to these institutions were for varying periods C.98 -C.107 Stanford University, California C.108-C.114 Gdttingen C.115-C.129 University of Michigan H. Davenport CSAC 112/3/86 Lectures and addresses 42 C.98-C.107 Stanford University, California, 1947-48, 1950. Davenport was invited by Gabor Szeg& (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.98-C.102 "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', Spp. ms. draft. C.102 of Course'; 3pp. ms. 'Examples on groups’; etc. Ip. ms. 'Groups Literature'; Ip. ms. 'Group Theory. Outline C.103 C.104 Programme of meeting of American Mathematical Society, April 1948, mentioning lecture by Davenport. "Selected Topics in the Geometry of Numbers', Summer Quarter, 1950. 67pp. typescript notes made by G. Hedrick. C.105-C.107 'Draft T. of nos Stanford', n.d. Contents of an envelope so inscribed. "Analytic Theory of Numbers’. C.105 Ms. draft of a course of lectures, variously sub-titled. ‘Additive number-theory' . C.106 Ms. draft for course of lectures, with note on first page ‘Analytic number theory ctd.'. C.107 'The Hardy-Littlewood method’. 22pp. ms. draft for lecture. H. Davenport CSAC 112/3/86 Lectures and addresses 43 C.108-C.114 Géttingen, 1954 and 1966. In 1966, Davenport was Gauss Professor der Mathematik an der Akademie der Wissenschaften zu G&ttingen (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 Guttingen 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.313 Lectures delivered May-August 1966, originally found together in an envelope labelled ‘Lectures G&ttingen'. All are in German. C.109 'Ausgewuhlte Fragen der Zahlentheorie' . 33pp. ms. draft. C.110 ‘Schlecht approximierbare Zahlen'. 32pp. ms. draft; Ip. ms. notes. C.111 'Die Verteilung der quadratischen Reste und Nichreste’ . 20pp. ms. draft. C.112. ‘Uber y? - x3! 9pp. ms. draft, paginated 38-46. C.113 'Gleichungen und Identitdten’. 19pp. ms. draft; 9pp. miscellaneous ms. notes and calculations (2pp. in English) . H. Davenport CSAC 112/3/86 Lectures and addresses 44 C.114 "Topics for Géttingen'. 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.115 "Analytic methods for Diophantine equations and Diophantine inequalities’, 1963. Bound photocopy of a course of lectures given at Michigan in the Fall Semester, 1962. Folder includes letter from publishers, 30 July 1963, outlining publication agreement. C.116-C.124 ‘Michigan Lectures’. Contents of a folder so inscribed. C.116 1962. "Analytic methods for Diophantine equations and inequalities’, 26pp. ms. draft. C.117 'Goldbach's Problem’. lépp. ms. draft. C.118 'Vinogradov's result on sums of 3 primes’. lépp. ms. draft. C.119-C.121 Variously titled and paginated shorter ms. drafts. 3 folders. C.122 Untitled ms. draft paginated 24-40A. C.123 Questions papers, etc. C.124 Original folder inscribed with calculations. H. Davenport CSAC 112/3/86 Lectures and addresses 45 C.125 "Modular fns' ‘Notes of seminar Mich. 1965?' Extensive ms. notes and calculations, originally found in a folder so inscribed. C.126-C.129 Series of 4 lectures, given 3-7 September 1968. C.126 'Diophantine approximation: an introductory survey’. 15pp. duplicated typescript with ms. corrections. C.127 ‘Badly approximable numbers’. llpp. duplicated typescript with ms. corrections. C.128 'Dirichlet's theorem’. 17pp. duplicated typescript with ms. corrections. C.129 "A problem of Diophantus' . 15pp. photocopy of ms. draft. C.130-C.158 SOCIETIES, CONFERENCES, ETC, The material here consists mainly of drafts for lectures given at conferences and to It does not however present a complete record societies, including undergraduate clubs. of Davenport's many visits and conferences. C.152-C.156 contain material which cannot be accurately dated, and C.157, C.158 consist: of invitations and programmes. Of particular interest is C.131, Davenport's address given at the prize day of his old school. C.130 'La géometrie des nombres', Brussels, 1946. 19pp. duplicated typescript draft (in French); two programmesof lectures, April-May 1946, of Institut des Hautes Etudes de Belgique. C.131 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, See also A.25. H. Davenport CSAC 112/3/86 Lectures and addresses 46 C132 'Some American Impressions', Presidential address to the Mathematical and Physical Society, University College, London, 29 October 1948. llpp. typescript draft. C.133, C.134 'G.H. Hardy', 1948 and n.d. 4pp. untitled ms. draft of a lecture, delivered in 1948. C.133 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 to an 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. C.135 'A great Oxford mathematician’ (H.J.S. Smith), Invariant Society, Oxford, 3 May 1950. llpp. typescript draft with ms. corrections. C.136, C.137 'Diophantine Approximation’, 1952, 1954. C.136 Colloquium, Greenwich, July 1952. 14pp. ms. draft of version delivered to British Mathematical C.137 Society, 3 March 1954. 7pp. ms. draft of version delivered to Oxford Mathematical App. ms. draft and notes re Diophantine approximation. App. ms. draft re lattice points. C.138 C.139 Rough outline of 'informal' talk at Queen Mary College, London, 4 February 1954. 2pp. ms. only. 'Problémes d'empilement et de recouvrement', Rome 1955. Alpp. typescript draft for lecture (in French). H. Davenport CSAC 112/3/86 C.140 C 141 Lectures and addresses 47 "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 withit. C.142 "Analytical number theory', ?1958. App. ms. notes also headed ‘Edinburgh + 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. C.143 'Equations in integers', New Pythagoreans, 21 January 1959. 6pp. ms. draft; ms. notes and calculations. Speech given at dinner of Mathematical and Physical Society, University College London, 5 March 1959. See also C.160. C.145 C.146 Spp. ms. notes. "Les quations diophantiennes 4 plusieurs variables' and 'Les inégalités diophantiennes a plusieurs variables', lectures delivered at the Faculté des Sciences, Université de Paris, 6 and 7 April 1959. Duplicated typescript drafts; 1959. letter of thanks from P, Dubreil, 20 July 'Dirichlet', 1959. 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 in 1860. H. Davenport CSAC 112/3/86 Lectures and addresses 48 C.147 'Diophantine approximation', lecture delivered at the British Mathe- matical Colloquium, Southampton, 13 April 1962. 15pp. ms. draft. C.148 Copy of report by Davenport on a visit to Poland, 18-30 March 1963, under arrangements for exchangevisits of scientists between Polish Academyof 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 C.149 "Irrational numbers', lecture to the Tensor Club, 6 February 1964. 14pp. ms. draft and calculations. C.150 ‘Report on visit to the University of Vienna’, 6-19 April 1964. Ip. ms. draft. 'Diophantische Gleichungen in mehreren Unbekannten', 15 April 1964, given during visit to Vienna. 2 ms. drafts, 6pp. and 14pp., with first page only of an early draft, all in German. C.151 "Quelques découvertes récentes dans la théorie des nombres', lecture given at the Université de Grenoble, 16 June 1967. Bound copy of lecture; 3pp. ms. notes entitled 'Brighton', found with it. H. Davenport CSAC 112/3/86 Lectures and addresses 49 C.152-C.156 Undated lectures for societies or conferences. C.152 "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. C.153 '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. C.157 delivered by Davenport, 1946 and 1968. Announcements of 2 London Mathematical Society lectures Programme of the Mathematical Association, 1949-50. C.158 of Mathematicians, 18 June 1949. Letter inviting Davenport to session of International Congress Programme of conference at Brussels, 1955. Programme of conference at Rome, 1968. H. Davenport CSAC 112/3/86 Lectures and addresses 50 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. Thefirst 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 'G of 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 keptin 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. C.159 'Marshall Hall's Theorem on Continued Fractions', n.d. 12pp. ms. draft, probably of a lecture, with Ip. ms. diagram. ‘General Functions', delivered to the Mathematical and Physical C.160 Society, University College London, 5 March 1959. lépp. ms. notes. See also C.144. 'Some doubts about mathematics', delivered to the 'Archimedeans', C.161 (a Cambridge undergraduate society), 23 November 1949. l0pp. typescript draft with ms. corrections. C.162 Mathematical and Physical Society dinner, UCL, 9 March 1956. 7pp. ms. draft for speech. C.163 'Progress in number-theory since 1930', n.d. 9pp. ms. draft of and notes fora talk. C.164 Professor of Mathematics, University College, London, 1945. "Inaugural lecture’, probably given on appointment as Astor Various ms. and typescript drafts. C.165 to the A.M.A., Berkeley, 24 January 1948. "Abstract of Lecture on the Geometry of Numbers', delivered 2pp. typescript. H. Davenport CSAC 112/3/86 51 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. C.171 57pp. typescript draft, with ms. corrections, for course of lectures, n.d. Note on first page 'P.G. lectures ?U.S.' C.172 "Abundant numbers', n.d. 12pp. ms. draft for lecture. C.173 ‘Solved and unsolved problems of mathematics’. 2 ms. drafts, 6pp. and Spp., of a talk. ‘Some unsolved problems’. 12pp. ms. draft of a talk. 'Solved and unsolved problems’. 7pp. typescript draft, with ms. corrections, of a lecture; Ip. ms. notes. H. Davenport CSAC 112/3/86 Lectures and addresses 52 C.174 ‘Some curious series’. 17pp. ms. draft of and notes and calculations for a talk. C.175 'Diophantine equations in many variables’ . 19pp. ms. draft for lecture. C.176 ' Jarnik and Walfisz'. 10pp. ms. draft for lecture; 3pp. ms. calculations. C.177, C.178 'Diophantine approximation’. C.177 Ip. ms. outline of course of 5 lectures. 2lpp. incomplete ms. draft of a series of lectures, paginated 1-13, 95-100. C.178 2lpp. miscellaneous ms. notes and calculations. C.179 "Geometry of Numbers’. llpp. ms. notes for 3 lectures. C.180 "Plans for G. of N. course’. 9pp. ms. notes and calculations. Included here isa Ip. ms. list of topics, probably for a lecture course, headed 'Hilbert'. C.181 9pp. untitled ms. draft of a lecture re 'some of the most important applications of analysis to the theory of numbers’. 3pp. untitled ms. draft of an after-dinner speech re nature of mathematical progress. H. Davenport CSAC 112/3/86 C.182-C.193 "Misc. math.' Lectures and addresses 53 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. The coefficients in a period of forms’. C.183 4pp. 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. C.185 5pp. paginated sequence of ms. notes and calculations. 3pp. sequence of ms. notes and calculations. 6pp. miscellaneous ms. notes and calculations. C.186 6pp. miscellaneous ms. draft and calculations. 3pp. ms. draft headed 'Chapter 6. Characters’. 5pp. miscellaneous ms. notes and calculations. C.187 'Zeta-function and L-functions'. 19pp. ms. draft. C.188 'Cyclotomy’. 13pp. ms. draft and calculations. C.189 5pp. sequence of ms. notes. 5pp. ms. draft and notes headed 'The Riemann-Zeta function’. 5pp. ms. draft and notes headed 'Alternative treatment of the Zeta- function’. 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. C.191 "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 oD 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 howeverthese do survive and in others there is more than one draft. Some correspondenceis 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. For additional correspondence and material exchanged with collaborators in publica- tions, see the relevant entries in Section G and also E 1 - E 15 (work with H. Hasse). D.1 'On certain exponential sums', 1933 (Bibliog. 5). 19pp. typescript draft (incomplete), with ms. corrections; 4pp. type- script draft. D2 D.3 'On the product of three linear homogeneous forms (II)', 1938 (Bibliog .25). 3lpp. typescript draft with ms. corrections; Ip. ms. calculations. 'On the product of three homogeneous linear forms(III)', 1939 (Bibliog. 26) 37pp. typescript draft with ms. corrections. D.4 'On Waring's problem for fourth powers', 1939 (Bibliog. 35). 30pp. ms. draft. H. Davenport CSAC 112/3/86 D.5-D.15 AdamsPrize Essay for 1939-40. Publications 56 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 D.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 : Ms., typescript and printed text of the essay. D.8-D.14 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. As the D.8-D.11 ‘Part One. On the Geometry of Numbers’. Introduction, Chapters I-VII, in 4 folders. D.12-D.14 'Part Two. On Waring's problem'. Introduction, Chapters I-VII, in 3 folders. D.15 Includes letter of 29 May 1941 informing Davenport of award. Brief correspondence re AdamsPrize Essay, 1941, 1942. D.16 'On sums ofpositive integral kth powers', with P. Erd&s, 1939 (Bibliog. 36). App. ms. draft (Erdés's hand). 'On linear fractional substitutions with large determinant', 1940 (Bibliog. 32). 6pp. ms. draft. H. Davenport CSAC 112/3/86 57 Publications "Note on the product of three homogeneous linear forms', 1941 (Bibliog. 39). App. ms. draft. D.19 | 'On a conjecture of Mordell concerning binary cubic forms', 1941 (Bibliog. 40). 12pp. typescript and ms. draft. D.20-D.22 'On sumsof positive integral kth powers', 1942 (Bibliog. 34). D.20 D.21 D.22 App. ms. notes. 18pp. ms. draft. épp. galley-proof, with ms. corrections. D.23 ‘On Waring's problem for fifth and sixth powers', 1942 (Bibliog. 37). l4pp. ms. draft. D.24, D.25 'On the minimum of a binary cubic form', 1943 (Bibliog. 41). D.24 D.25 4 ms. drafts, 6pp., 7pp., 10pp. and Ilpp. Ip. ms. calculations, 14pp. typescript draft. D.26, D.27 'On the product of three homogeneous linear forms (IV)', 1943 (Bibliog. 42). D.26 D.27 Ms. draft paginated 1-45 (p.24 missing). 32pp. ms. draft. D.28 'On the minimum of a ternary cubic form', 1944 (Bibliog. 43). 10pp. ms. draft. H. Davenport CSAC 112/3/86 Publications 58 D.29 'The reduction of a binary cubic form (I)', 1945 (Bibliog. 45). 8pp. typescript draft with ms. corrections. D.30 'The reduction of a binary cubic form (II)', 1945 (Bibliog. 46). 12pp. ms. draft; 8pp. typescript draft with ms. corrections. D.31 'On the minimum of x3 ty? +z3', 1946 (Bibliog. 44). 2 ms. drafts, 5pp. and 6pp. D.32 ‘Simultaneous Diophantine approximation’, with K. Mahler, 1946 (Bibliog. 47). 8pp. ms. draft; 6pp. typescript draft. D.33 'On a theorem of Tschebotareff', 1946 (Bibliog. 48). 2 ms. drafts, each 7pp. D.34 'On indefinite quadratic forms in five variables’, with H. Heilbronn, 1946 (Bibliog. 49). 12pp. ms. draft (Heilbronn's hand); 9pp. ms. draft. D.35 'The product of n homogeneouslinear forms', 1946 (Bibliog. 50). 8pp. ms. draft. D.36 'Non-homogeneous binary quadratic forms', 1946 (Bibliog. 51). 7pp. and 8pp. ms. drafts. H. Davenport CSAC 112/3/86 D.37 "Theory of Numbers', 1946-47. Publications 59 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. The book was published in 1952 as 'The higher arithmetic’. 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. 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’ . 5pp. typescript draft, probably of introduction to the book. 6pp. untitled typescript draft, paginated 15-20. D.38 'On the product of three non-homogeneous linear forms', 1947 (Bibliog. 52). 20pp. typescript draft, with ms. corrections. D.39 ‘Asymmetric inequalities for non-homogeneous linear forms', with H. Heilbronn, 1947 (Bibliog. 55). Letter to Heilbronn, 27 June 1946, re modification to a proof. 5pp. untitled ms. draft, partially paginated, labelled '55A'. Included here is 'A problem in the geometry of numbers', with H. Heilbronn, 6pp. ms. draft labelled ‘essentially published', probably 1947 or a little later. D.40 'On a theorem of Markoff', 1947 (Bibliog. 57). 5pp. ms. draft. D.41 '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. 'final' draft. H. Davenport CSAC 112/3/86 Publications 60 D.42 'The Geometry of Numbers', 1947 (Bibliog. 59). App. typescript draft. D.43 'A historical note’, 1947 (Bibliog. 60). 2pp. typescript draft with ms. corrections. D.44 'Non-homogeneous binary quadratic forms II', 1947 (Bibliog. 61). l4pp. typescript draft with ms. corrections. D.45 "Non-homogeneous binary quadratic forms III', 1947 (Bibliog. 62). 9pp. typescript draft. D 46 'Sur une extension d'un théoréme de Minkowski’, 1947 ‘Bibliog. 64). 2pp. ms. draft. D.47, D.48 'Non-homogeneous binary quadratic forms V', 1947 (Bibliog 66). D.47 D.48 Ilpp. ms. notes and calculations, Ip. labelled 'Prelim to 66'. 24pp. ms. draft. D.49 'The geometry of numbers', 1947 (Bibliog. 67). 10pp. typescript draft. D.50 'Non-homogeneous ternary quadratic forms', 1948 (Bibliog. 63). 34pp. ms. draft. D.51 'Note on indefinite ternary quadratic forms', 1948 (Bibliog. 71). App. typescript draft with ms. corrections. H. Davenport CSAC 112/3/86 Publ ications 61 D.52 'On the equation ax? + by? +cz2 = O', 1948 (Bibliog. 72). 5pp. typescript draft with ms. corrections, with Ip. ms. addition. D.53 'On indefinite ternary quadratic forms', 1949 (Bibliog. 56) l4pp. typescript draft with ms. corrections, with Ip. ms. addition. D 54 'On the product of two powerseries', with G. Pélya, 1949 (Bibliog. 69). Opp. typescript draft; 10pp. ms. and typescript draft. D.55 ‘On a result of Wald', with G. Pélya, 1949 (unpublished). 2 ms. drafts, 6pp. and Spp.; letter from Wald, 19 September 1949, to Pélya. D.56 'A divisor problem', 1949 (Bibliog. 73). llpp. ms. draft. D.57 'On the series for L(1)', 1949 (Bibliog. 73). 5pp. typescript draft with ms. corrections. D.58 'On a theorem of Khintchine', 1950 (Bibliog. 68). 18pp. typescript draft with ms. corrections. D.59 ‘Indefinite binary quadratic forms, and Euclid's algorithm in real quadratic fields', 1950 (Bibliog. 70). 25pp. typescript draft with ms. corrections. D.60-D.62 '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. Continued H. Davenport CSAC 112/3/86 Publications 62 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 (J193)! 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. D.63 'Euclid's algorithm in cubic fields of negative discriminant', 1950 (Bibliog. 76). 23pp. typescript draft with ms. corrections, with 7pp. ms. additions. D.64-D.66 ‘Indefinite binary quadratic forms', 1950 (Bibliog. 77). D.64 D.65 13pp. ms. draft, labelled 'prelim to 77'. llpp. and 6pp. ms. drafts, both labelled 'prelim to 77'. D.66 editor, T.W. Chaundy, re corrections. 12pp. typescript draft with ms. corrections, with note from D. 67 D.68 'Diophantine inequalities with an infinity of solutions', with C.A. Rogers, 1950 (Bibliog. 79). 59pp. typescript draft with ms. corrections; Ip. ms. list of contents. 'On the critical determinants of cylinders', with C.A. Rogers, 1950 (Bibliog. 81). 5pp. typescript draft with ms. corrections. H. Davenport CSAC 112/3/86 Publications 63 D.69 'Euclid's algorithm in certain quartic fields', 1950 (Bibliog. 82). 34pp. typescript draft with ms. corrections. D.70 "Note on a binary quartic form', 1950 (Bibliog. 83). l0pp. typescript draft with ms. corrections. D.71 'L'algorithme d'Euclide dans certains corps algébriques', 1950 (Bibliog. 84). 7pp. typescript draft, in English, labelled 'basis of lecture at Paris congress Sept 1949'; pp. ms. draft (in French). D.72 'Study and Research in Mathematics', 1950 (Bibliog. 85). 9pp. typescript draft. D.73 'Sums of three positive cubes', 1950 (Bibliog. 87). 6pp. ms. draft; 7pp. typescript draft. D.74, D.75 ‘Recent progress in the geometry of numbers’, 1950 (Bibliog. 91). D.74 5pp. ms. draft with 3pp. ms. notes; I5pp. ms. draft labelled 'Second draft (used at lecture)’ and 'Congress lecture’. D.75 13pp. typescript draft with ms. corrections. D.76 'On a principle of Lipschitz', 1951 (Bibliog. 88). 5pp. typescript draft labelled 'prelim to 88', with 4pp. ms. notes; 6pp. typescript draft. D.77 'On the class-number of binary cubic forms (I)', 1951 (Bibliog. 89). 8pp. typescript draft, entitled 'On binary cubic forms', labelled 'preliminary to 89'; Ilpp. typescript draft. H. Davenport CSAC 112/3/86 Publ ications D.78 'On the class-number of binary cubic forms (II)', 1951 (Bibliog. 90). 7pp. typescript draft. 'On sequencesofpositive integers', with P. Erdds, 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 I'espace 4 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. Erdés, 1952 (Bibliog. 93). 8pp. photocopy of typescript draft. 'Linear forms associated with an algebraic number-field', 1952 (Bibliog. 94). 15pp. ms. and typescript draft. "Note on a result of Chalk', 1952 (Bibliog. 95). 12pp. photocopy of typescript draft. 'The covering of n dimensional space by spheres', with R.P. Bambah, 1952 (Bibliog. 97). 7pp. ms. and typescript draft. 'The covering of space by spheres', 1952 (Bibliog. 99). 20pp. typescript draft. H. Davenport CSAC 112/3/86 65 D.87 "Simultaneous Diophantine approximation', 1952 (Bibliog. 100). Publications 15pp. typescript draft with ms. corrections. D.88 'The distribution of quadratic and higher residues’, with P. Erdés, 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, reachedits fifth 'It has undoubtedly been a source of joy and inspiration edition in 1982. to many mathematicians both amateur and professional’ (Memoir, p.167). See C.86 for coverillustration 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 Professor B. J. Birch has contributed (February 1986) the following explanatory note: ‘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. Probably the material was "tested" in lectures at UCL (and maybe Bangor).' D.90 lishers, 1951-57. Correspondence with Hutchinson's University Library, pub- Correspondence with reviewers, L. Schoenfeld and P.T. Bateman, 1953, with Ip. ms. note of where reviews appeared. D.91, D.92 1952-61, arrangedin alphabetical sequence. General correspondence with colleagues and others, D.91 B-G D.92 L-W H. Davenport CSAC 112/3/86 Publications 66 D.93 'The minimal points of a positive definite quadratic form', with G.L. Watson, 1954 (Bibliog. 103). Spp. typescript draft with ms. corrections. D.94 'Simultaneous Diophantine approximation’, 1954 (Bibliog. 104). 34pp. typescript draft. D.95 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. D.96 'Simultaneous Diophantine approximation’, 1954 (Bibliog. 106). 5pp. typescript draft. D.97, D.98 'On a theorem of Furtwdngler', 1955 (Bibliog. 105). D.97 D.98 15pp. ms. draft. 19pp. typescript draft with ms. corrections. D.99-D.101 'Products of inhomogeneous linear forms', with H.P.F. Swinnerton- Dyer, 1955 (Bibliog. 107). 2 letters from H.P.F. Swinnerton-Dyer, 1954, re publication D.99 of paper, with 2pp. ms. notes and calculations entitled 'n = 5, r= 1, s = 2', and labelled 're 107’. 5pp. untitled ms. draft, with 2pp. ms. calculations. D.100 'first version’. 33pp. untitled ms. draft (Swinnerton-Dyer's hand), labelled D.101 44pp. typescript draft with ms. corrections. H. Davenport CSAC 112/3/86 68 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. D.117 2 ms. drafts, 5pp. and IIpp. D.118 and 6pp. 2 ms. drafts on same subject, 7pp. (with 4pp. ms. notes) D.119 Miscellaneous ms. notes, drafts and calculations. D.120 Ms. notes by Birch. D.121 'The work of the Fields medallists. Dr. K.F. Roth', 1958 (Bibliog. 121). 5pp. typescript draft with ms. corrections; set of page-proofs. D.122-D.128 'Cubic forms in 32 variables', 1959 (Bibliog. 116). D.122 74pp. ms. draft. D.123, D.124 different ms. corrections. 2 copies of 75pp. typescript draft, both with D.125 25pp. ms. draft, paginated 73-97, and headed '8 Synthesis’ . D.126 l4pp. ms. draft headed 'Cubic Forms. "Absolute" lemmas’. H. Davenport CSAC 112/3/86 Publications 69 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. D.132 D.133 D.134 '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. 'On a theorem of P. J. Cohen', 1960 (Bibliog. 125). 2 ms. drafts, 7pp. and 8pp. ‘Uber einige nevere Fortschritte der additiven Zahlentheorie', 1960 (Bibliog. 127). 2 ms. drafts, 15pp. and lépp. D.135, D.136 'On Weyl's inequality and Waring's problem for cubes', with S. Chowla, 1961 (Bibliog. 124). D.135 29pp. ms. draft. D.136 8pp. ms. draft 're 124' and Spp. ms. draft. H. Davenport CSAC 112/3/86 Publications 70 D.137 ‘A note on binary cubic forms', 1961 (Bibliog. 126). 2 ms. drafts, 9pp. and 1lpp; correspondence. D.138 ‘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 l6épp. ms. draft, with Spp. ms. notes. D.142 'A note on Diophantine approximation’, 1962 (Bibliog. 133). 7pp. typescript draft with ms. corrections. D.143 ‘Exponential sums in many variables', with D.J. Lewis, 1962 (Bibliog. 135). 34pp. ms. draft with covering note to 'Bryan' (Birch). D.144 'Cubic forms in sixteen variables’, 1963 (Bibliog. 134). Set of galley-proofs with ms. corrections. D.145, D.146 'Notes on congruences(I)', with D.J. Lewis, 1963 (Bibliog. 136). D.145 2 typescript drafts with ms. corrections, 9pp. and 12pp. D.146 Set of page~proofs with ms. corrections; 2pp. ms. notes. H. Davenport CSAC 112/3/86 Publications 7 D.147 "Notes on congruences(II), with D.J. Lewis, 1963 (Bibliog. 137). 15pp. ms. draft with corrections. D.148 "Homogeneous additive equations’, with D.J. Lewis, 1963 (Bibliog. 138). 4épp. ms. draft with corrections; note to publisher. D.149 'A problematic identity’, 1963 (Bibliog. 140). 6pp. ms. draft. D.150 '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. D.152 work for this paper (or for Bibliog. 145). 5pp. ms. notes by A. Schinzel, dated 9.3.64, possibly D.153 'Non-homog. cubic eqns', with D.J. Lewis, 1964 (Bibliog. 148). 10pp. ms. draft, beginning: 'This is an account of a paper by Lewis and myself which has been submitted to PLMS'. D.154, D.155 'On a theorem of Mrs. Turén', 1965 (Bibliog. 153). D.154 version without corrections. 8pp. heavily-corrected ms. draft, and photocopyof original D.155 covering letter to B.J. Birch, 8 July 1964. 7pp. photocopy of ms. draft with ms. corrections, and a D.156 12 = x3! 21965. 6pp. ms. draft with 2pp. ms. notes, labelled 'Early version, eventually published as 159’. H. Davenport CSAC 112/3/86 Publications 72 7pp. untitled ms. draft, labelled 'm/s of 158 (first folio missing)', 21966. D.158 "Looking back', 1966 (Bibliog. 162). lépp. typescript with ms. corrections. D.159 D.160 '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. D.161 'Cubic equations of additive type', with D.J. Lewis, 1966 (Bibliog. 167). 68pp. typescript draft with ms. corrections. D.162 "Notes on congruences III', with D.J. Lewis, 1966 (Bibliog. 169). 8pp. typescript draft, with Ip. ms. list of references and Ip. ms. calculations. 'Eine Bemerkung Uber Dirichlets L-Funktionen', 1966 (Bibliog. 171). 17pp. ms. draft with corrections. D.164-D.169 'Diophantine approximation and sums of roots of unity', with A. Schinzel, 1967 (Bibliog. 166). D.164 November 1965-October 1966. Correspondence, chiefly with A. Schinzel, re paper, D.165 Miscellaneous ms. notes and drafts. H. Davenport CSAC 112/3/86 Publications 73 D.166 'A problem connected with Diophantine approximation’. 6épp. ms. draft. 'Diophantine approximation and roots of unity’. 8pp. ms. draft. D.167 21pp. ms. draft with corrections, labelled 'Versions of 166'. D.168 15pp. 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.170 includes covering note from publisher, August 1967, returning 'dead' material (now at D.170-D.177). D.175 App. typescript index with ms. corrections. D.176, D.177 Corrected proofs. Photocopy of original ms. draft, with ms. corrections for D.178-D.182 revised version. D.178 includes letter from Davenport, 4 April 1969, to Yu. V. Linnik re corrections, also mentioning that he was in hospital. 5 folders. D.183 'On the large sieve method', with E. Bombieri, 1968 (Bibliog. 172). 17pp. ms. draft with corrections. For correspondence and further drafts see G.37. H. Davenport CSAC 112/3/86 D.184, D.185 Publications 74 '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 Spp. and 4pp. Ms. notes and calculations, including 2 paginated sequences, 6pp. notes by Landau. D.185 5pp. 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. D.188 'A theorem on linear forms', with W.M. Schmidt, 1968 (Bibliog. 177). 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’. D.191 6pp. and IlIpp. drafts and calculations on 'Thue's Theorem’. D.192 26pp. ms. draft. D.193 Corrected version of D.192 (photocopy). D.194, D.195 'Some inequalities involving trigonometrical polynomials’, with E. Bombieri, 1969 (Bibliog. 181). For correspondence re paper see G. 38. D.194 23pp. ms. draft. D.195 E. Bombieri. l4pp. photocopy of 'note on the large sieve inequality’, with Early version of Bibliog. 181. H. Davenport CSAC 112/3/86 Publications 75 D.196, D.197 ‘Correspondence with Baker relevant to 182, and two m/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). 6pp. ms. draft. ‘Simultaneous equations of additive type’, with D.J. Lewis, 1969 (Bibliog. 184). 105pp. photocopy of ms. draft with corrections; 4pp. ms. summary. Biographical article on G.H. Hardy commissioned by 'The Encyclopedia Americana’, 1969. Correspondence, January, February 1969; 2pp. ms. draft. See C.133, C.134 for Davenport's lecture material on Hardy. D.198 D.199 D.200 D.201-D.203 'On writing mathematical papers', 1969 (unpublished). D.201 Correspondence, 1966, 1969; 2pp. ms. notes. D.202 Background material (printed matter). D.203 from L.J. Mordell, June 1969. 23pp. typescript draft with covering letter to Mrs. Davenport Letters to Mrs. Davenport re paper from J.W.S. Cassels, October 1969, and V. Armitage, February 1970. H. Davenport CSAC 112/3/86 Publications 76 D.204 'Two additive equations', with D.J. Lewis, 1971 (Bibliog. 186). 32pp. photocopy of typescript draft with ms. corrections. D.205 "Homogeneous quadratic equations', 1971 (Bibliog. 194). 10pp. photocopy of typescript draft. D.206 'Gaps between valuesof positive definite quadratic forms', with D.J. Lewis, 1971 (Bibliog. 195). 27pp. photocopy of typescript draft; Ip. instructions to printer; Ip. corrections. D.207 '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 camein reply to this query.’ 3pp. ms. note by Davenport; letter from Halberstam returning it to him, March 1968. 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. D.208 Reviews by Davenport, 1938-64. Arranged in chronological sequence by date of the publication of the work reviewed. Material includes review of L. J. Mordell's inaugural lecture as Sadleirian Professor at Cambridge, published 1947. D.209 3pp. incomplete typescript draft of letter concerning a book, not by Davenport, n.d. H. Davenport CSAC 112/3/86 Publications 77 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. Part only; for full version see A.10. App. typescript index, with ms. corrections by B.J. Birch. H. Davenport CSAC 112/3/86 78 SECTION E RESEARCH NOTES AND DRAFTS E.1 -E.135 E.1 -E.15 COLLABORATION WITH HE LMUT HASSE, 1933-36 E.16 -E.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 E.1-E.15 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). is Hasse's work but there is some correspondence and a draft for a further collaborative Most of the material here paper. Davenport's other collaborators are represented in Sections D and G. For further correspondence with Hasse, see G.116-G.122. E.1, E.2 Letters from Hasse, May 1933-November 1935, chiefly concerning the joint paper, mostly in English. E.1 1933, 1934 E.2 1935 E.3 ‘Gaussian sumsin finite fields', by H. Davenport and H. Hasse. 12pp. typescript and ms. draft with ms. corrections. E.4, E.5 Miscellaneous ms. notes and calculations by Hasse, in English and German. 2 folders. E.4 includes sets of notes dated 28 September 1933 and 10 December 1935. E.6 7pp. ms. draft, in German, by Hasse. H. Davenport CSAC 112/3/86 Research notes and drafts 79 E.7-E.15 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.83 TITLED AND UNTITLED DRAFTS Probably many of these drafts were intended to form lectures or papers for publica - tion, while others may be no more than extensive notes. A number of these are untitled and very few are dated. Dated titled drafts E.16 'For a single irreducible polynomial’, 1934. Spp. ms. 'Tschebotareff's constant (/2)N...-- ', 1939. 2pp. ms. with covering note to L. J. Mordell. Folder also includes 2 additional, untitled drafts, each 3pp. E.18 'Three fourth powers', 1943. App. ms., and 8pp. ms. labelled 'Revised version 17.10.43'. E.19 ‘Four fourth powers' (continuation of E.18). 6pp. ms. with Ip. ms. calculations. Folder also includes 3pp. ms. notes, found with above, entitled '5 4-th powers’. E.20 'On X12 +57) 1946. 7pp. ms. H. Davenport CSAC 112/3/86 80 E.2] ‘Direct proof of Marshall Hall's Theorem’, 1956. Research notes and drafts 2pp. ms., with 2pp. ms. entitled 'M. Hall. 9 May 1956. Difference sets', dated Undated titled drafts E.22 "Polynomials mod x*' 7pp. ms. E.23 ‘Polynomials (mod p)’. App. ms. E.24 'Vinogradov's work on the addition of primes’. lépp. ms. E.25 ‘Primes in arithmetic progression’. 3pp. ms. with Ip. ms. notes. E.26 'On reduced positive definite quadratic forms' . 9pp. typescript, with Ip. ms. notes. E.27 "Indefinite quadratic forms’. 18pp. ms., with Ip. ms. notes. E.28 'The quadratic character’. 2pp. ms. with 3pp. ms. notes and calculations. E.29 "Characters (mod M)'. App. ms., with 10pp. untitled ms. draft and notes. H. Davenport CSAC 112/3/86 81 Research notes and drafts E.30 'The Weierstrassian equation y2 = 4x3 - gx -93'- 6pp. ms. E.31 'On a problem of Fekete’. 3pp. ms. E.32 'An introd. to Turén's book’. 10pp. ms. with reprint of paper presented by P. Turan and 6pp. ms. notes and calculations. E.33 'Turén-Halész'. Opp. ms. E.34 'Units:in algebraic numberfields'. 10pp. ms., with bibliography . E.35 "Distribution of Farey fractions’. 13pp. ms. E.36 'Diophantine equations in many variables’ . 9Ypp. ms. E,37 "Exponential sums’ . 3pp. ms., found in an envelope labelled '185? Dirichlet Rome vol. to appear’, possibly an early draft for Bibliog. 185. E.38 'On the cubic exponential sum'. 7pp. ms. H. Davenport CSAC 112/3/86 Research notes and drafts E.39 "Notes on Littlewood's Problem’. 3pp. ms. with 4pp. ms. calculations. 'Littlewood's Problem’. 2pp. ms. 82 Included here is a further ms. draft, with notes, of the sametitle, and 3pp. draft on 'The distribution of certain fractional parts’. E.40 'The critical lattices ...'. 6épp. ms. with Ip. ms. notes. E.41 'The field k(V5)'. Spp. ms. E.42 "Units'. 10pp. ms., with 6pp. notes. E.43 ‘Analytic treatments of the Kloosterman sums’ . 3pp. ms. E.44 ‘Binary cubic forms with D< O'. Opp. ms. E.45 'The product of three complex linear forms’ . 2pp. ms. E.46 'Four linear forms. Type I’. 2lpp. ms., with 4pp. ms. notes. Folder also includes '( ) of Type I', 13pp. ms. found with the above. H. Davenport CSAC 112/3/86 Research notes and drafts E.47 'The congruence ...' App. ms. 'A modification of Cauchy's inequality’. 3pp. ms. "Successive minima for Ly, ly, L3'. 2pp. ms. 'Macbeath's proof of Chalk's theorem’. Ip. ms. ‘Simplest version of Rogers’. App. ms. "Ingham'. Spp. ms. 'A lemma concerning pairs of integer points’. Spp. ms. "Uniform distribution’. llpp. ms., with 10pp. ms. notes. 'On the values of zeta (4 +it)'. 5pp. ms., witha ms. note ‘Birch’. 'Quartic’. 2pp. ms., with 5pp. ms. notes and calculations. H. Davenport CSAC 112/3/86 Research notes and drafts E.57 'Modified definition of V,,'. App. ms. E.58 "Note on some conjectures of Ramanujan’. Ip. ms., paginated '102'. E.59 "Extension of Heilbronn's Theorem’. 13pp. ms., variously paginated, possibly connected with Bibliog. 176. E.60 'Charaktere der Restklassengruppe mod (xk, p)'. 2pp. ms., in German. E.6] "Squares in A.P.'. Spp. ms. E.62 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 E.63-E.65 Contents of an unlabelled binder, consisting of a sequence of unpaginated ms. drafts, possibly for a course of lectures, with some ms. notes. These have been divided into separate folders for ease of reference, and kept in their original order. E.64 l4pp. ms. 'The gamma function’; 22pp. ms. ‘Elliptic functions’. E.65 some paginated. 11pp. ms. ‘Modular functions’; miscellaneous ms. notes, H. Davenport CSAC 112/3/86 Research notes and drafts E.66-E.68 ‘Miscellaneous math. mss and notes’. 85 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); 6pp. 'Hermite's process E.66 of continued reduction’; 5pp. miscellaneous notes and calculations; 9pp. 'Cassels S.D.A.'. 3pp. untitled; 2pp. re '3 k-th powers', with covering E.67 note; 8pp. (in another hand) ‘Markoff numbers'; 9pp. 'Quadratic and higher residues'; 6pp. tables. App. on 'various problems', 13 October 1954; 4pp. with E.68 2pp. notes, on ‘Simultaneous Diophantine Approximation’; 4pp. on 'On lattice points in n-dimensional star bodies’; 3pp. and Spp. un- titled. Miscellaneous bibliographies, including 2 with titles: "Waring etc. in Math. Rev.' and 'Sieve methods’. 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. In view 13 folders. E.69 E.70 Untitled drafts E.71-E.83 H. Davenport CSAC 112/3/86 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.87 3 exercise books, labelled ‘Cassels 1', ‘Cassels 2' and 'Cassels 3', containing notes and calculations. E.88 Exercise book, labelled 'Math.', tf 4 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. E.90 "Elaboration of previous argument'. 2pp. ms. E.9] 'Ternary cubic’. 12pp. ms. notes and calculations; 2 ms. tables entitled 'Properly primitive ternary forms’. E.92 'Various equivalences between character-sums' . 2pp. ms. notes with 3pp. ms. calculations. E.93 'Zero of Emden Function’. 2pp. ms. notes. E.94 Miscellaneous shorter notes, all titled. Five items. H. Davenport CSAC 112/3/86 Research notes and drafts Untitled notes and calculations 87 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. Groups of notes have been kept together; E.102 contains miscellaneous single sheets. 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 Davenportat 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 'Lecture attended in Brussels on Alternating Algebra, May 1946'. Ip. ms. notes. E.104-E.117 'Lectures attended', 1951-63 and undated. Contents of a folder so inscribed. E.104 1951-52 Seminar talks and lectures by P. Erdds. E.105 C.A. Rogers, H.A. Heilbronn. 1952 Seminar talks and lectures by K. Mahler, P. Erdés, E.106 C.A. Rogers. 1953 E.107 E.108 1954 1955 E.109 A. Oppenheim. 1956 Lectures by K.F. Roth, K. Mahler, J.H.H. Chalk, Seminar talks and lectures by K. Mahler, L. Few. Lectures by T. Estermann, A. Renyi. Lectures by W.B. Pennington, B.J. Birch, H. Davenport CSAC 112/3/86 m o “ Research notes and drafts 88 110 . Erdés, G.L. Watson. 1956-57 Lectures by W.B. Pennington, J.W.S. Cassels, E2171 1957 Lectures by G.C. Shepherd, Danicic, W.J. LeVeque. E.112 1958-59 Lectures by L.J. Mordell, P. Erdés, A.E. Ingham. E.113 1960-63 Lectures by B.J. Birch, K. Mahler, P. Erd&s. E.114 L. Few, Gelfond. n.d. Seminar talks and lectures by E.S. Barnes, P. Erd&s, E.115 n.d. 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, Shorter unidentified notes. E.117 Included here is Mrs. Davenport's list of contents of material now at E.103-E.117. Davenport's notes on work by others Although in many cases Davenport gave the date of publication of the Therefore they have work, few of these notes are themselves dated. 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. E.118, E.119 Material relating to Blichfeldt, collected or made by Davenport. See also C.27-C.29. E.118 2 letters from A. Braver, 1932, to Blichfeldt. 'Remarks on work of Blichfeldt', n.d. (¢.1947-50). 2pp. ms. notes by Davenport. App. miscellaneous ms. notes on Blichfeldt, made by Davenport, n.d. (c. 1947-50). 'Various topics in the theory of numbers', 1953-54. 6pp. typescript draft of a lecture by Davenport, containing material on 'Blichfeldt's Principle’. E.119 Ms. notes, some dated 1920-22, not in Davenport's hand. H. Davenport CSAC 112/3/86 Research notes and drafts 89 E.120 'Richard Braver. A note on systems of homogeneous algebraic equations’, n.d. 3pp. ms. on paper published by Braver in 1945. E.121 " Jacobi’, n.d. 8pp. ms. draft and Ip. ms. calculations. E.122 "Mordell's work', n.d. App. ms. 'Pélya's Problem in Amer. Math Monthly', n.d. 3pp. ms. on paper by G. Pélya. E.123 ‘Rademacher. Riemann-von Mangoldt Theorem', 7 July 1959. Spp. ms. 'R. Remak. Uber die Minkowskische Reduktion der definiten quadratischen Formen’. 3pp. ms. on paper published by Remak in 1938. E.124 'J.M. Vinogradov. Ona general theorem concerning the distribution of the residues and non-residues of powers', n.d. 6pp. ms. on paper published by Vinogradov in 1927. 'J.V. Whitworth', n.d. Ip. ms. notes re Whitworth's thesis, 1947, for MSc. at Manchester University. E.125, £.126 "Miscellaneous math mss’. Contents of a folder so inscribed. B.125 Ms. notes on various topics made from Hardy -Littlewood. Ms. notes on work by Hecke, including ‘Uber analytische funktionen und Verteilung von Zahlen mod eins' (published 1921). Ms. notes on Lerche's formula. H. Davenport CSAC 112/3/86 Research notes and drafts 90 E.126 analytische Zahlentheorie’ . "Landau. Bedeutung der Pfeifferschen Methode fur 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. E.127 'A valuation of some information concerning finite fields', by J.H. Conway, n.d. l4pp. typescript. E.128 'Research Problems’, by H.T. Croft, August 1967. 'This set of problems went through various editions, and was published (in collaboration with R.K. Guy) in c.1983, under the title "Unsolved Problems in Intuitive Mathematics"'. B.J. Birch, February 1986.) (Information from Professor 28pp. duplicated typescript . 'Problems (mostly geometrical)', by H.T. Croft, n.d. 7pp. duplicated typescript . H. Davenport CSAC 112/3/86 Research notes and drafts 91 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. E.129 'The Theory of the Distribution of Primes. Chapter I’, n.d. E.130 ‘Chapter I', n.d. E.13] ‘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', nied. E.132 'Difference of two positive definite quadratic forms', by D. Ridout, n.d. (4pp. ms.). E.133 Miscellaneous ms. notes by C.A. Rogers, n.d. E.134 Photocopies of ms. drafts by H.P.F. Swinnerton-Dyer, n.d. E.135 Unidentified. H. Davenport CSAC 112/3/86 92 SECTION F FACULTY OF MATHEMATICS, CAMBRIDGE F.1 - F.17 Fit F.6 F./7 =F.9 GENERAL COMMITTEES NEEDS OF FACULTY AND SUB-DEPARTMENTS F.10-F.12 APPOINTMENTS, 1960-69 F.13 REQUESTS FOR POST-GRADUATE PLACES F.14-F.16 EXAMINATION PAPERS F.17 MISCELLANEOUS F.1-F.6 F.1-F.3 GENERAL COMMITTEES, 1959-65 Policy Committee of the Faculty of Mathematics, 1959-64. Notices of meetings, agendas, minutes and reports, arranged in chronological order. F. 1 F.2 1959-60 1961-63 F.3 1964-65 and n.d. F.4 Pure Mathematics Lectures Committee, 1962 Notice of meeting and proposals for lecture list. F.5, F.6 Faculty Board of Mathematics, 1964-65. Correspondence and committee minutes, mainly re newly- rao created Department of Applied Mathematics and Theoretical Physics (D.A.M.T.P.). F.6 October 1964. Notes and correspondencere affairs of D.A.M.T.P., H. Davenport CSAC 112/3/86 93 Faculty of Mathematics, Cambridge F.7-F.9 NEEDS OF FACULTY AND SUB-DEPARTMENTS, 1959-65 These papers largely consist of Statements of Needs of various depart - ments, in various areas, such as teaching staff, new equipment, etc. F.7 1959-60 F.8 1961-64 P.7 1965 and n.d. F.10-F.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 F.11 1962 F:12 1963-69 F.13 REQUESTS FOR POST-GRADUATE PLACES In alphabetical order, 1964, 1965 only. F.14-F.16 EXAMINATION PAPERS F.14 F.15 2pp. untitled ms. list of examination questions, n.d. 2pp. ms. list of examination questions, with covering letter from J.W.S. Cassels, 1961, re suitability of one question. Copies of examination papers for Mathematical Tripos, Part III, 1964 and 1967. 1964 1967 Papers | - VI Paper 13. Diophantine Approximation H. Davenport CSAC 112/3/86 Faculty of Mathematics, Cambridge 94 F.17 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 95 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. Bombieri, H.A. Heilbronn, K. Mahler and L.J. Mordell, while no correspondence with G.H. Hardy, howeverbrief, lacks its characteristic quality. Davenport's long association with German mathematicians, many of whom became refugeesin 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. G.1 Adams, A 1964 Mathematical puzzles on integers. G.2 Aitken, A.C. 1956, 1959-60 Inequalities. €.3 Ankeny, N.C. A research student of Davenport at Stanford 1947-48, later at Princeton and M.1.T. 1948-52, 1958 Mainly on number theory. G.4 Ap Simon, H.G. n.d. probably 1957 llpp. 'Notes on a Sunday Times brain teaser’. H. Davenport CSAC 112/3/86 Correspondence 96 G.5-G.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 1955-57 1958-61 1962-68 Atkin, A.O.L. Austin, M.C G.10-G.12 Bambah, R.P. 1946, 1961, 1964 195] 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 1954 G.11 Arrangements for Bambah's Fellowship at St. John's College, Cambridge; includes list of publications and draft paper on 'Four Squares’. G.12 result). Barnes, E.S. Basu, S.K. 1961, 1965 (a letter from a pupil of Bambah on mathematical 1949, 1964 1947, 1966, 1968 A student of Davenport in London, 1945-47. Bateman, P.T 1950, 1963-65 1950 letter is re paper by R.P. Bambah (q.v.). Correspondence 1963-65 is on general research problems, appointments, publica- tions, etc. Behrend, F.A. 1933-34, 1939 A German mathematician who was obliged to leave for Britain in 1939. list of publications, etc. Correspondence 1939 includes curriculum vitae, testimonials, H. Davenport CSAC 112/3/86 97 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. G.20 Birch, B.J. 1959, 1966 Brief correspondence only. frequent collaborators; he contributed on account of his 'Work on the 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 Londo. G.21 and publication. 1947, November-December. Frequent letters on results G..22 paper G.23 1948, January-July. Similar correspondence, includes draft October-December. 1949, 1953-54. G.24 Blundon, W.J. 1956-57 Mainly publication of Blundon's papers on 'multiple covering’, and ‘packing’; includes figures. G.25 G.26 Boas, R.P. Jnr. Bohr, H 1948 1947, 1949 Davenport's publications in Acta Mathematica. G.27 Bollobas, B. 1963-65, 1967 Mainly arrangements for Bollob&s to come to Trinity College for academic year 1963-64 and including Davenport's recommendation and ‘account of studies' during year at Cambridge. H. Davenport CSAC 112/3/86 Correspondence 98 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, 163, 172, 181. See Memoir, pp.164-165). 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 1965, September-December G.32 and drafts, on ‘prime numbers' paper and on ‘large sieve’ paper (published 1968, see G.38). Continuing correspondence G..33 G.34 G.35 G.36 1966, January-April 1966, June-September Includes letter from H. Halberstam. 1966, October-December Mainly on sieve paper. Extensive notes by Davenport kept with 1966 correspondence. 1967 G.37 and correspondence on polynomials (leading up to collaborative paper published in 1969). Includes revised version of 'large sieve method’ July, 1968, January-July G .38 of 'large sieve’ paper, and a 7pp. ms. by Davenport 'The case N§ small’, and letters of comment. Includes arrangements re publication G.39 Fields medal at International Mathematical Congress, Vancouver, 1974. Also includes press-cutting re award to Bombieri of the 1969 H. Davenport CSAC 112/3/86 Correspondence 99 Bosanquet, L.S. Brandon, R.W. 1948, 1949 1953 Braver, A. 1931, and Braver, R. 1953 Brothers, both German refugee mathematicians. G.40 G.4l G.42 G.43 G.44 G.45 Brjuno, A.D. Broadbent, A. Brown, D.S. 4-colour problem. 1966 1963 1965 1965 1954 1934 1963, 1965, 1968 Correspondence 1954 196] G.46 Buckell, J.F. Four Square Representation. G.47 G.48 G.49 Buhl, G. Bullen, K.E. Burgess, D.A. A former research student of Davenport at U.C.L. on ‘character sums’. G.50 Burt, C. Printing of journals and especially Mathematika . G.51 Capildeo, R. A former research student. One letter only. G.52-G.56 Cassels, J.W.S. 1946-69 and n.d. General correspondence on research and publications. G.52 G.53 November-December 1946, 1947 1948, 1949, 1951 G.54 1954, 1955, 1956 Continued H. Davenport CSAC 112/3/86 100 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’. Chalk, 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. G.59, G.60 Chandrasekhar, S. G.59 personal news. 1946-48 G.60 1964 n.d. 1946-48, 1964 Onfunctional equations; also includes some Chase, R.E. Proof of unique factorisation. Chatelet, F. Chatland, H. Mainly on collaborative paper (Bibliog. 74). 1962 1946 1948-49 G.64-G.66 Chowla, S. Chowla, a distinguished Indian pure mathematician, studied at Cambridge, where his supervisor was J.E. Littlewood. He returned to academic posts in India, moving to USA in 1948. correspondence is sporadic and does not include any of Davenport's replies. The surviving 1933-63 1933-34 andn.d. 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. Includes testimonials for Chowla Letter of 16 February 1933 Some of the undated G.65 1947-49 G.66 1962, 1963. 1958-60 Mainly re collaborative paper (Bibliog. 124), H. Davenport CSAC 112/3/86 Correspondence 101 G.67 Cohen, P.J. 1959, 1960, 1965 Research and publications. Gi68, G.69 Cohn, H. 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 G.70 Cole, A.J. 1952-53 A research student of Davenport in London; mainly re thesis. G.71 Collingwood, E. 1965 Centenary of London Mathematical Society; includes reprint of article on subject by Collingwood. G.72 Courant, R. 1934, 1945, 1947 Early correspondenceis from Géttingen, with news of German mathe- maticians. is renewing contact after the war. Courant left for America in August 1934. Later correspondence G.73-G.76 Coxeter, H.M.S. 1928-59 An undergraduate friend of Davenport at Cambridge, using his youthful nickname of 'Dave' in the letter of 1928 and signing his own letters 'Donald'. Includes some personal news as well as mathematical research. G:73 3pp. 'Prop' by Coxeter. 1928, 1929, 1932 (from Coxeter's mother), 1935. Includes G.74 G.75 G.76 1939 1945-48 1951-53, 1958+59 G.77 Cridland, N. 1954-56 Packing of small circles. and passed on by him to Davenport. Enquiry originally addressed to S.T. Shovelton H. Davenport CSAC 112/3/86 Correspondence 102 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 G.84, G.85 Dolciani, M.P. 1963 1938 1964-65 1953-55 G.84 Davenport on theory of numbers. Arrangements to spend sabbatical leave working with G.85 Miscellaneous ms. notes and drafts. Draim, N.A. various dates 1950-65 DuVal, P. One letter only, from Princeton. Mainly mathematical but refers to J. von Neumann's proposed visit to Cambridge. 1935 Dyson, F.J. Includes laudatory report by Davenport on ‘fellowship thesis by F.J. Dyson: "Two problems in the theory of numbers". 1942, 1946 Eichler, M. Oneletter only. Elliott, P.D.T.A. 1962 1966 H. Davenport CSAC 112/3/86 Correspondence 103 G.91 Ennola, V. 1957-59 Research, draft paper on lattice constants. Erdés, P. 1934, 1960, 1961-65, 1969 Although Erdés and Davenport collaborated on many publications 1936-63, the surviving correspondence is very meagre and is mainly from Erdés on various mathematical discoveries. Correspondence 1960is enquiry re Erd&s's problem on sets of congruences. Errera, A. Estermann, T. Davenport's ms. letter only. Evelyn, J. Fenna, D. 1953, 1955 1949 1950, 1960 1958 Paper on 'Simultaneous diophantine approximation to series’. Fjellstedt, L. Davenport's carbon only, on a paperby Fiellstedt. 1956 Flanders, H. Flett, T.M. G.100 Godwin, H.J. 1969 1949-50 1955 Davenport's unpublished 1938 work on inhomogeneous|inear forms. G.101 Goodstein, R.L. 1950 Appreciation of Davenport's paper 'Study and research in mathematics’ (Bibliog. 85). G.102 Grunwald, G. G.103 Guy, R.K. Hadamard, J. Brief exchanges only. 1939 1958, 1964 1947, 1952, n.d. H. Davenport CSAC 112/3/86 Correspondence 104 G.105 Halberstam, H. 1957, 1962-68 Research, publications, appointments. G.106 Haldane, J.B.S. 1952 One letter only, on an inequality, with Ip. attached calculations by Davenport headed 'Haldane’. G.107 Hall, M. 1947-48, 1958 General correspondence on research and publications, including collaborative paper (Bibliog. 72). G.108 Hall, P. One letter only. G.109-G.114 Hardy, G.H. 1965 1938-47 Hardy, one of the most distinguished British mathematiciansof 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. 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. G.109 1938, 1939 G.110 1940 Appeal on behalf of H. Heilbronn. G.111 undergraduate here called Dyson who is very promising’ [F.J. Dyson]. Undated letter (perhaps 1942) refers to 'an 1941, n.d. G.112 of 'Hardy-Wright' but including a little general mathematical information . 1944, May~December and undated. Mainly on revisions G.113 October, and miscellaneous comments on other parts of book. Davenport's letter and revision of Chapter 24, 1944 G.114. 1945, 1946, 1947 H. Davenport CSAC 112/3/86 Correspondence 105 Grid Haselgrove, C.B. 1960 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 Gull? 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.120 1935 C21 1936, 1938, 1939 Gi 1946, 1947, 1949, 1952, 1963, 1967 (death of Hasse's wife). G.123-G.142 Heilbronn, H.A. and others 1934-67 When Heilbronn 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 Guttingen 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). A fuller account of Heilbronn's career, including his friendship with Davenport, can be found in the Memoir by J.W.S. Cassels and A. Fréhlich (Biographical Memoirs of Fellows of the Royal Society, 22, 1976), an offprint of which is included at G.123. Continued H. Davenport CSAC 112/3/86 G.123-G.142 (Cont'd.) Correspondence 106 G.123 only, re Heilbronn's acceptance of Bevan Fellowship at Trinity). Includes a letter from L.J. Mordell; 1935. (card 1934 G.124 1939 Twoletters only. G.125 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. 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, Almost all the documents in G.133-G.140 are concerned with 124-25). 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. In 1963 Heilbronn resigned from his G.133 headed 'University expansion. 1959 Quantity or quality’. Heilbronn's letter to A.U.T., December 1959, 1960, January-March. G.134 to Chairman, U.G.C. (Sir Keith, later Lord, Murray) and draft questionnaire. Includes draft letter and memorandum 1960 G.135 university teachers in mathematics’ circulated April 1960 by Heilbronn and Davenport. Material re 'Questionnaire on recruitment of H. Davenport CSAC 112/3/86 Correspondence 107 G.136 Cambridge, sent to Davenport in answer to questionnaire. Replies and information from colleagues in 1960, May G.137 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 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. ) Correspondence re proposed conference Davenport was asked to chair G.140 Memorandum', 'Notes on the questionnaire’, etc. Miscellaneous notes and drafts for 'Second 1960 G.141 1962-63 G.142 1964, 1965, 1967 Brief correspondence only. G.143 Heinhold, J. Henstock, R. G.145 Hirsch, K.A. 1948 1963 1952 G.146 Hlawka, E. 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’. G.147 Hodge, W.D.V. 1954, 1965 Correspondence 1954 is re P. Erdds. G.148 Hofreiter, N. G.149 Hooley, C. G.150 Hopf, H. 1951 1963, 1965 1955, 1958 H. Davenport CSAC 112/3/86 Correspondence 108 G.151 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.155-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'. G.155 1936-44 G.156 1945-48 G.157 1950, 1957 G.158 Jarnik, V. 1946 A Czech mathematician, renewing contact with UK colleagues. G.159 G.160 Jenkins, G.M. 1961 Kanagasabapathy, P. Research and publications. 1951-52, 1962-63, 1968 G.16l Kemmer, N. 1956 On 'Physics teaching in Britain’. G.162 Kestelman, H. 1947, 1948 Letters to Davenport in California, with news of UCL and Britain. G.163 Khan, N.A. 1954 Knapowski, S. 1959, 1963, 1966 Polish research student at Cambridge. H. Davenport CSAC 112/3/86 G.165 Correspondence 109 1934-35 and undated, 1942 Kober, H. A German refugee mathematician. Breslau, correspondence 1942 from Birmingham. Correspondence 1930sis from G.166 Kosambi, D.D. G.167 Kreisel, G. Lang, S. 1961 1958 1963-64 Comments on Davenport's research notes and publications. p p G.189 Ledermann, W. Includes 6pp. ms. note by Davenport 'A question concerning quadratic forms’ . 1958 G.170 Leech, J. G.17] Lehmer, D.H. G.172, G.173 LeVeque, W.J. 1958 1948 1961, 1963 1961] G.172 Topical History of the Theory of Numbers'. report (not favourable) of American Mathematical Society Committee, Davenport's draft comments, etc. Correspondence on proposed 'Compilation of a Includes draft proposal, 1963 Includes 6pp. ms. note by Davenport, 'On Weyl's G.173 criterion for uniform distribution' later published jointly with LeVeque and Erdis (Bibliog. 142) and a related note by LeVeque on Weyl's criterion. G.174 Levy, M. Delay lines. 1950 H. Davenport CSAC 112/3/86 Correspondence 110 G.175-G.184 Lewis, D.J. 1957-68 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 correspondencereflects 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.177 1961 G .178 G 179 1962 (Bibliog. 136, 137, 139), visits, lectures 1963 (Bibliog. 137, 138, 139, 141, 145) G . 180 1964 (Bibliog. 145, 148) G.181 1965 G.182 1966 (Bibliog. 167, 169) G.183 CG. 184 1967 1968 G.185 G.186 G.187 Linnik, Yu. V. General correspondence, including Russian translation of Davenport's Multiplicative number theory. 1950-69 (not all dated) Littlewood, D.E. Littlewood, J.E. Card only. 1952-53, 1955 1931 H. Davenport CSAC 112/3/86 Correspondence 111 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 G.193 Mack, J. 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.194 Mahler was interned). 1933-34, 1940 (one letter only, from Isle of Man where G.195 1945 (Bibliog. 47), 1946 G.196 1947-49 G.197 1950-51, 1953 G.198 papers for, Mathematika. 1954-55 Includes some reference to the founding of,and G.199 1956-57 G.200 1958-59, 1961 1962-63. G.201 Letter of 4 March 1963 announces Mahler's decision to accept research chair at Australian National University, Canberra. 1967 (one letter only). H. Davenport CSAC 112/3/86 G.202 Mann, H.B. Matthews, K.R. Mayer, A. G.203 G.204 G.205 G.206 Correspondence 112 n.d. 1963-66 1950 A German refugee, thanking Davenport for help with publication . Mendelsohn, N.S. 1949 Milne, E.A. 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, a distinguished mathematician of American origin, with a 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 Davenport was among his closest friends. until his death in 1972. 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). Mordell succeeded Hardy in the Sadleirian Chair at 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). 1930 G.209 take up the 'splendid opportunity’ to go to Marburg to work with and teach English to Hasse. Letter of 27 November suggests Davenport should H. Davenport CSAC 112/3/86 Correspondence 113 G.210 1931 Research and publications, mainly on congruences. G.21] 1932-33 G.212 1934, 1935 G.213 1936 (one letter only), 1938, 1939 (one letter only). G.214 1942, 1943, 1944 G.215 1945, 1946 G.216 1947 (includes comments on Bibliog. 56), 1948 G.217 of G.H. Hardy. 1949 (not all dated). Some refer to death and obituaries G.218 1950 G.219 195] G.220 G.22] G.222 G.223 1952 1953 1954 1955 G .224 1956 G.225 1957 G .226 1958 G.227 1959 1960 (one letter only), 1961 (includes draft paper by Mordell G.228 'On a Pellian Equation Conjecture’, anda 2pp. untitled ms. note by Davenport). G.229 1962 G .230 1963, 1964 (includes draft paper by Mordell) G.231 1965 G .232 1967 (one letter only), 1968 (one letter only) G orrespon dence 114 H. Davenport CSAC 112/3/86 G. 233 Cc 234 G. 235 Muses, C.A. Neugebauer, O. Niven, I. 236 O'Baoghaill, M. Triangle of minimum area. .237 238 Olds, D: Oppenheim, A. 1959 1938 1956 1954 1958 1946-52 1958 1959 1958 1954-56 1960 Correspondence and research notes, mainly on quadratic forms, also on new University of Malaya, Singapore. Zo) Orde, H.L.S. Prime factors of a large number. . 240 Ormonde, Marquess of Equations in high numbers, with 2pp. draft reply. . 241 Ostrowski, A. 'Schubfachprinzip' . Pedoe, D. Pennington, W.B. . 242 243 244 245 . 246 Includes 1]pp. draft paper by Pennington 'On Widder's inversion formula’. Perron, O. Philipp, W. Littlewood's problem. Phillips, E.G. 1946 1964 1951 H. Davenport CSAC 112/3/86 Correspondence 115 G.247 Pitman, J. 1962, 1965 and n.d. Research, appointments. research notes on 'Cubic Problem’, 4pp. note by Davenport on 'A Theorem of Rado! and 7pp. ms. draft by Davenport on 'Miss Pitman's simplification' of Bibliog. 119. Includes material made available by B.J. Birch: G.248-G.251 and Polya, S. Polya, G. Davenport and his wife made the acquaintance of George and Stella Polya on their Stanford visit 1947-48, and remained lifelong friends. 1947-64 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.251 1956-64 Various dates, shorter exchanges. G.252 Popova, H. Includes draft research papers by Popova and correspondence from A.S. Besicovitch. 1952 G.253-G .255 Prasad, A.V. 1946-68 Prasad was a research student of Davenport in London, working on theory of numbers, before returning to India. 1946-50 1952, 1954 1955, 1968 (re thesis) G.253 G.254 G.255 Pye, D.R. 1947 Rado, R. various dates 1934-68 Rado was a refugee mathematician in Cambridge in 1933. His letter to Davenport on his appointment to the Chair of Pure Mathematics at Reading in 1954 expresses his gratitude for Davenport's consistent support . G.256 G.257 H. Davenport CSAC 112/3/86 G.258 G.259 Correspondence 116 Ramanujam, C.P. 1962, 1965 Rankin, R. various dates 1950-63 G.260 Redei, L. 1949, 1953, 1959 Hungarian mathematician. G.26] Remak, R. G.262 Rendle, A.B. Comments on paper. G.263 Reuter, G.E.H. Richert, H-E. Ridout, D. Robinson, G. de B. G.265 G.266 | 1938 1954 n.d. 1954 1958, 1959 1941 Invitation to contribute a book on number theory to new series ‘Mathematical Expositions’ . G.267 Robinson, R.M. Minkowski's results on packing of tetrahedra. by J.W.S. Cassels. 1959-60 Includes comments G.268-G .278 Rogers, C.A. and others 1945-69 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 wasfirst author of the Royal Society Memoir of Davenport. He collaborated with Davenport on several papers 1947-50 G.268 only). 1945, appointment as Demonstrator at UCL, 1946 (one letter G.269 news, sent to Davenport in USA. 1947 Frequent reports on research and departmental G.270 (Bibliog. 70, 71, 73, 79). 1948 Departmental news, research, publications H. Davenport CSAC 112/3/86 Correspondence 117 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). 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 A research student of Mordell, and later of Davenport, who later worked in USA. G.279 inhomogeneous minima of indefinite Hermitian forms’. 1951, 1953 Includes research note by Rogers 'The G.280 1954-55, 1963, 1964 G.281 Romanoff, N. 1935, 1937 G.282, G.283 Roth, K.F. various dates 1951-57, 1964-65 Roth was a research student and later a colleague of Davenport at UCL and wrote collaborative papers with him (see Memoir, p.163). 1951 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 1954, 1956-57, 1964, 1965 H. Davenport CSAC 112/3/86 G.284 G.285 Correspondence 118 Rumney, M. 1947, 1964 Sadler, D.H. 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. 1928, 1940-46 Card of G.286 Saelman, B. Problem in elliptic integrals. Salié, H. Sawyer, D.B. Scherk, P. G.287 G.288 G.289 G.290 1952 1931, 1933 1957, 1961 1951 Theorem on addition of residue classes. Schinzel, A. A Polish mathematician and graduate student of Davenport at Cambridge, who collaborated with him on several papers. 1962, 1966-69 G.291 Schmid, H.L. G.292 Schmidt, F.K. 1937 1960 G.293, G.294 Schmidt, W.M. Schmidt spent part of the academic year 1966-67 in Cambridge and wrote several collaborative papers with Davenport. 1965-69 G .293 185, 188). G.294 20pp . Correspondence, mainly on publications (Bibliog. 173, 183, Ms. drafts by Davenport for work with Schmidt, 4pp. and G.295 Schnitzer, F. 1952-57 Various research problems. H. Davenport CSAC 112/3/86 Correspondence 119 G.296 Schoenfeld, L. . 1967 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 1951 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. G.301 Professorship for Davenport at Gittingen, May-July 1966. notices of lectures and draft in German of Bibliog. 171. C.108-C.114. Correspondence and arrangements re Gauss 1965-66 Includes See also G.302 1966-68 Siegel's recollections. G.303 hand: 'Siegel', S5pp. dated 20 and 22 July 1966; 'Siegel', 5pp. dated 26 July 1966; 'Siegel At Kneser's', 5pp. dated 27 July 1966. These are ms. accounts in Davenport's G.304 Sierpinski, W. 1959, 1963, 1964 Mainly re publications in Acta Arithmetica, including Bibliog. 149. G.305 Smith, C.A.B. G.306 Smith, G.S. 1951 1953, 1955 Research problems and notes, mainly fractions for irrational numbers. G.307 Spencer, D.C. 1959 Includes comment by J.W.S. Cassels. H. Davenport CSAC 112 /3/86 Correspondence 120 G.308 Sprenger, E. 1953 Paper on 'Odd numbers', redrafted by Davenport. Sprindzuk, V.G. G.310 Srinivasan, B.R. G.31] Stark, H. G.312 Steen, S.W.P. Research note. G.313 Steward, G.C. Translation of a Russian paper by Kotelnikoff. G.314 Stoller, G. Waring's problem. 1967, 1969 1962 1966-67 n.d. 1952 1960 G.315 Swinnerton-Dyer, H.P.F. 1953-57 Correspondence, research notes and problems (not all dated) including collaborative paper (Bibliog. 107). G.316 Szegd, G. 1948-49, 1956 Correspondence 1956 includes letters re symposia at 1958 Congress and a memorandum by S. Bergman on complex variables. G.317 Szekeres, G. G.318 Szele, T. 1958 1951 Includes research note on 'Davenport's theorem’. G.319 Taussky-Todd, O. 1950, 1957 G.320 Titchmarsh, E.C. Oneletter only. G.321 Todd, J.A. 1957 1945 H. Davenport CSAC 112/3/86 Correspondence 121 G.322 Tschebotareff, G.N. 1955 Re recent death of his father. G.323 Turan, P. and Turan, V. 1934, 1947, 1964-67 Research and publications, including contributions to memorial volume for E. Landau (Bibliog. 172). G.324 Ursell, H.D. G.325 Uspensky, J.V. G.326 Vallance, L.S. 1969 1947 1955-57 G.327 van der Corput, J.G. and van der Corput, J. 1946-48, 1952-53, 1961 Visits, publications, research. Includes a little personal correspondence. G.328 van der Pol, B. G.328A van der Waerden, B.L. Comments on draft papers by Davenport. G.329 Vandiver, H.S. G.330-G .334 Varnavides, P.L. 1953 1932-33 1949 1947-60 Varnavides was a research student of Davenport at London and subse- quently worked abroad. publications and includes drafts of papers submitted by Varnavides. The correspondence is mainly on research and G.330 1947-48 G.331 1950-51 G .332 1952-54 G .333 1955-56 Includes various drafts of papers on quadratic forms. G.334 «1957, 1959-60 H. Davenport CSAC 112/3/86 Correspondence hz2 G.335, G.336 Walfisz, A. 1930-33, 1936, 1949-57 Pre-war corres pondenceis from Radosé; post-war correspondenceis from Tiflis. G.,335 1930, 1931 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 ofreprints. 1949, 1954, 1956-57 Brief correspondence, mainly on G.337 Ward, G.W. Contemporary of Davenport at Trinity. G.338-G . 344 Watson, G.L. 1964 1950-60 After taking a mathematics degree at Trinity, Cambridge, in 1930, Watson entered the Indian Civil Service. On returning to Britain, he 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. Despite the paucity of letters G..338 G.339 1950 1951 G .340 1952 Includes research note. G .341 (Bibliog. 103), and other research notes. 1953 Includes drafts, etc. for collaborative paper G .342 research notes). 1954 (one letter only), 1955 (includes drafts for papers and G .343 (includes research note). 1956 (one letter only), 1957 (includes research note), 1958 Includes draft papers, and 5pp. ms. draft for G.344 part of Bibliog. 119. 1959 1960 H. Davenport CSAC 112/3/86 Correspondence 123 G.345 Watson, G.N. 1933, 1945 Correspondence 1933, ona 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. G.346 Whitehart, F.E. 1950 Elementary proof of the prime number theorem. G.347 Whiteley, J.N. c.1959-60 Research and publications, including draft papers. Few letters dated. G.348 Whyte, L.L. 1949, 1952 Correspondenceand notes re points on a sphere. G.349 Williams, W.L.G. Invitation to Davenport to a Chair at McGill. G.350 Wonham, W.M. Random noise. 1948 1959 G.351 Wright, E.M. 1952, 1957 Correspondence 1952 is re 3rd edition of 'Hardy and Wright’ Introduction to the theory of numbers (published 1954). G.352 Youngs, J.W.T. G.353 Zeeman, E.C. 1958 1965 Proposal for National Mathematics Research Centre. G.354 Zervos, S.P. Mathematical papers of P. Zervos (father of S.P.). G.355 Zulauf, A. Research and publications on prime numbers. G.356 Zygmund, A. Includes note by Davenport in reply to problem. 1952 1954-56 1954 G.357 Shorter scientific correspondence (not indexed). In alphabetical order. H. Davenport CSAC 112/3/86 Correspondence 124 G.358-G.372 References, appointments, theses, requests for advice 15 folders, in alphabetical order. A B (1) B (2) C E G .358 G.359 @ . 360 O Q . 361 2 a . 362 2 0 O . 363 a M 364 o Q 365 G.366 G.367 G.368 G.369 G.370 Ww (1) G.371 W (2) G.372 G.373 'Cranks' (Davenport's description). Some with replies by Davenport, or notes for a reply by colleagues. 1 box. H. Davenport CSAC 112/3/86 125 BIBLIOGRAPHY Reproduced with permission from Biographical Memoirs of Fellows of the Royal Society, 17, 1971, 187-192. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) 1931. On the distribution of quadratic residues (mod p). 7. Lond. Math. Soc. 6, 49-54. 1931. 1932. 1932. 1933. 1933. On Dirichlet’s L-functions. 7. Lond. Math. Soc. 6, 198-202. Onthedistribution of the /th powerresidues (mod p). 7. Lond. Math. Soc. 7, 117-121. Ona generalization of Euler’s function ¢(n). 7. Lond. Math. Soc. 7, 290-296. Oncertain exponential sums. 7. fiir. Math. 169, 158-176. Onthe distribution of quadratic residues (mod /) (second paper). 7. Lond. Math. Soc. 8, 46-52. 1933. 1934. 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Lewis & A. ScuinzeL.) Quadratic Diophantine equations with a parameter. Acta Arithmetica, 11, 353-358. Onf*(£) —g2(t). K. Norske Vid. Selskabs Forh. 38, 86-87. Problems of packing and covering. Rend. Sem. Mat. Univ. e Polytec. di Torino, 24, 41-48. The London Mathematical Society. Nature, Lond. 207, 350-351. Looking back. 7. Lond. Math. Soc. 41, 1-10. (With E. Bomsrert.) Small differences between prime numbers. Proc. Royal Soc. Lond. A, 293, 1-18. Quelques problémes d’approximation diophantienne. Rend. Sem. Mat. Milano, 35, 3-8. (With A. Scuivzet.) A note oncertain arithmetical constants. Illinois F. Math. 10, 181-185. (With A. ScuinzEL.) Diophantine approximation and sums ofroots of unity. Math. Annalen, 169, 118-135. (With D. J. Lewis.) Cubic equations of additive type. Phil. Trans. Royal Soc. Lond. A, 261, 97-136. H. Davenport CSAC 112/3/86 130 Bibliography (168) 1966 . (With H. Hauserstam.) The value of a trigonometrical polynomial at well spaced points. 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Acta Arithmetica, 14, 209-223. A. E. Ingham. Nature, Lond. 216, 311. (With H. Hatserstram.) Corrigendum and addendum. Mathematika, 14, : (171) 1966. (172) 1968. (173) 1967. (174) 1968. (175) (176) (177) (178) (179) (180) (181) 1968. 1967. 1968. 1967. 1967. 1968. 1969. (182) 1969. 229-232. A note on Thue’s theorem. Mathematika, 15, 76-87. (With E. Bomarert.) Some inequalities involving trigonometrical polynomials. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. 23 (Fasc. 2), 223-241. (With A. Baxer.) The equations 3x?—2 = y? and 8x2—7 = 22. Quart. F. Math. (2), 20, 129-137. , (183) 1969. (With W. M. Scummpt.) Approximation to real numbers by algebraic integers. (184) 1969. (185) 1970. (186) 1971. (187) (188) 1968. 1970. (189) 1970. (190) 1969. (191) 1971. (192) 1971. (193) (194) (195) 1971. 1971. Acta Arithmetica, 15, 393-416. (With D. J. Lewss.) Simultaneous equations of additive type. Phil. Trans. Royal Soc. Lond. A, 264, 557-595. (With W. M. Scumipr.) Dirichlet’s theorem on Diophantine approximation. Istituto Nazionale di alta Mathematica. London: Symposia mathematica, 4, Academic Press, pp. 113-132. (With D. J. Lewts.) Two additive equations. Proceedings of Symposia in Pure Maths. (Houston), 12, 74-98. (With H. Harperstam.) Corrigendum. Michigan Math. F. 15, 505. (With W. M. Scummpt.) Supplement to a theorem on linear forms. Colloquia Mathematica Societatis Fanos Bolyai, 2. Number Theory. Debrecen, Hungary, 1968. Budapest and Amsterdam,pp. 15-25. (With W. M. Scumivr.) Dirichlet’s theorem on Diophantine approximation, Il. Acta Arithmetica, 16, 413-424. (With H. Hertsronn.) On the density of discriminants of cubicfields. Bull. ‘Lond. Math. Soc. 1, 345-348. (With H. HertBronn.) On the density of discriminants of cubic fields, IT. Proc. R. Soc. Lond. A, 322, 405-420. A combinatorial problem connected with differential equations, IT. (Edited by A. Schinzel.) Acta Arithmetica, 17, 363-372. A determinantof linear forms. Mathematika, 18, 100-104. Homogeneous quadratic equations. Mathematika, 18, 1-4. (With D. J. Lewis.) Values of positive definite forms in many variables. Acta Arithmetica. (In the press.) H. Davenport CSAC 112/3/86 INDEX OF CORRESPONDENTS 13] ADAMS, A. ADAMS, J. F. G.1 G.136 ADRIAN, Edgar Douglas, Baron A.61, A.76 AITKEN, Alexander Craig AITKEN, Sir Robert ANKENY, Nesmith C. ANNAN, Noél Gilroy, Baron AP SIMON, HH. ARCHBOLD, J. G. W. ARMITAGE, J. Vernon ASHBY, Eric, Baron ATKIN, A. O. L. AUSTIN, M. C. BAILEY, W. N. BAKER, Alan BAMBAH, RR. P. BARNES, Eric S. BASU, S._ BATEMAN, Paul T. K. BEHREND, Felix A. BERLOWITZ, Bernard BERNDT, Bruce 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 A.57, A.62 A.77, D.196 G.10-G.12 G.13 G.14 D.90, G.15 G.16 G.17 G.37 BESICOVITCH, Abram Samoilovitch BILLING, Gunnar BIRCH, Bryan John BLANEY, Hugh BLUNDON, W. J. A.42, A.62, A.77, G.18, G.252 See also B. 57 G.19 A.77, D.112-D.116, D.143, D.155, D.210-D.212, G.20, G.92 G.21-G.23 G.24 H. Davenport CSAC 112/3/86 Index of correspondents BOAS, R. P. Jnr. 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 BUCKELL, J. F. BUHL, G. BULLEN, Keith Edward BURGESS, David Albert BURKILL, John Charles BURNABY, John BURT, Sir Cyril BUTLER, Richard Austen, Baron CAPILDEO, R. CASSELS, John William Scott CHALK, John H. H. CHAMPERNOWNE, Arthur CHANDRASEKHAR,, Lalitha CHAN DRASEKHAR, Subrahmanyan CHASE, R. E. 132 G.25 G.26 A.77, G.27 G.28-G.39 A.57, A.62, G.40, G.152 A.62 G.136 A.70 G.4l E.118, G.42 G.A2 G.43 A.62, G.44 A.77 G.45 G.46 G.47 G.48 A.77, G.A9 A.62, A.77 A.39 G.50 A.77 G.51, G.242 A.62, D.203, F.15, G.52-G.56, G.267, G.307 G.57 G.58 G.60 A.47, A.62, A.70, A.78, G.59, G.60 G.6l H. Davenport CSAC 112/3/86 133 Index of correspondents CHATELET, Frangois CHATLAND, Harold CHAUNDY, Theodore William CHOWLA, S. CLEMMOW, P.-C. COHEN, Paul Joseph COHN, Harvey COLE, 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 CRIDLAND, Nigel DAINTON, Frederick Sydney, Baron DAVIES, Merton DAVIS, Clive S. de BRUIJN, N. G. DELAUNAY,B. DERRY, Douglas DE WITTE, Paul DIENES, Paul DIRAC, Gabriel A. DOLCIANI, Mary Patricia DRAIM, Nick A. DRAZIN, Michael DUBREIL, Paul DUFF, Patrick William DUMIR, Vishwa Chander G.62 D.60, G.63 D.66 G.64-G.66 G.136 G.67 A.78, G.68, G.69 G.70 A.78, G.71 D.91, E.127 A.57, A.78 D.91 A.47, A.70 G.72 A.62, A.70, A.78, G.73- G.76 A.47, G.73 G.77 A.74 G.78 G.79 G.80 G.81 A.63, A.79, G.82 A.79 G.268 G.83 G.84, G.85 A.79, D.91, G.86 A.63 C.145 A.79 G.12 H. Davenport CSAC 112/3/86 DuVAL, Patrick DYSON, Freeman John Index of correspondents 134 EDDINGTON, Sir Arthur Stanley EDKINS, C. W. EGGLESTON, H. G. EICHLER, M. ELLIOTT, Peter D. T. A. ENNOLA, Veikko ERDOS, Paul ERRERA, Alfred ESTERMANN, T. EVANS, Benjamin Ifor, Baron EVELYN, Sir John (Jack) FENNA, Donald FEW,L. FJELLSTEDT, L. FLANDERS, Harley FLETT, T. FRIEDLANDER, F._ FROHLICH, Albrecht M. G. GILLIS, J. GODWIN, H. GOODSTEIN, R. GRUNWALD, G. GUY, Richard K. J. LL. A.79, G.87 See also A.53 G.88 See B.58 A.24, A.39, A47 A.63 G.89 A.80, G.90 G.91 A.80, D.91, G.92 See also D.210 G.93 A.80 See also G.94 G.276 G.95 G.96 G.254 G.97 G.98 G.99 G.136 A.63 A.47 G.100 G.101 G.102 G.103 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._ HASSE, Helmut B. HAYMAN, Walter Kurt HEAP, A. HEILBRONN, Hans Arnold HEINHOLD, J. HENSTOCK, Ralph HIRSCH, Kurt A. HLAWKA, Edmund HODGE, Sir William (Vallance Douglas) HODGKIN, Sir Alan (Lloyd) HOFREITER, N. HOLLOND, H. A. HOOLEY, Colin HOPF, Heinz HOWARTH, Leslie HUA, Loo-Keng 135 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 G.115 A.81, E.1, E.2, G.116-G.122 See also G.114, G 285, G.303 A.63, A.81 A.38 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.151 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. JEFFERY, G. B. JEFFREYS, Bertha, Lady JENKINS, G. M. JONES, W. Burton KANAGASABAPATHY, P. KEMMER, Nicholas KESTELMAN, Hyman KHAN, Nisar Ahmed KITSON CLARK, George Sidney Roberts KNAPOWSKI, S. KOBER, Hermann KOSAMBI, D._ D. KREISEL, G. LANDAU, Edmund LANDAU, Marianne LANG, Serge LEDERMANN, Walter LEECH, John LEHMER, Dick H. LEHMER, Emma 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 See D.184, D.185 D.185 G.168 G.169 G.170 G.17] A.82 LEVEQUE, William J. (Bill) LEVY, M. G.172, G.173 G.174 H Davenport CSAC 112/3/86 Index of correspondents LEWIS, Donald J. LIGHTHILL, Sir (Michael) James LINFOOT, Edward Hubert LINNIK, Yu.V. LITTLEWOOD, D. LITTLEWOOD, John Edensor LOGAN, M. LONDON MATHEMATICAL SOCIETY E. McANDREW, H. MACBEATH, Alexander Murray McCREA, Sir William Hunter MACK, John MCLEOD, J. B. MAHLER, Kurt MANN, Heinrich B. MARTIN, Sir David Christie MATTHEWS, K._ R. MAYER, Alfred MENDELSOUN, Nathan S. MILLER, J. C. P. MILNE, Edward Arthur MONTGOMERY, Hugh Lowell MORDELL, Louis Joel MORRELL, A. J. H. MOTT, Sir Nevill Francis MURDOCH, B._ H. MUSES, C. A. 137 G.175-G.184 A.82 A.48, A.57 A.82, G.185 G.186 A.Al, A.82, E.131, G.187 A.64 A.60, A.90, G.188, G.189 G.190 A.64, G.191 A.64 G.192 G.193 A.57, A.64, A.83, G 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 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 A. 64 A. 64 G.83 G.233 H. Davenport CSAC 112/3/86 Index of correspondents 138 NEUGEBAUER, O. NEUMANN, Bernhard NIVEN, Ivan NYHOLM, Sir Ronald (Sydney) O'BAOGHAILL, Mary OFFORD, A. Cyril OLDS, Douglas OPPENHEIM, Tan Sri Sir Alexander ORDE, H. L. S. ORMONDE, James Arthur Norman Butler, 6th Marquess of OSTROWSKI, A. PAGE, Arthur PARS, Leonard Alan PEARSON, Egon PEDOE, D. G .234 A. 64 G.235 A.7] G.236 A.49, A.64, A.83 G .237 G .238 G.239 G.240 G.241 A.57 A.39, A.84 A.7] G.242 PENNINGTON, W. B. A.65, A.71, G.243 PERRON, Oskar PHILIPP, Walter PHILLIPS, Edgar G. PITMAN, Jane POLKINGHORNE, John Charlton POLYA, George POLYA,Stella POPOVA, Helen PRASAD, A. Vindhyachal PYE, Sir David (Randall) G.244 G.245 A.65, G.246 A.84, G.247 A.84 D.92, G.248-G.251 See also D.55 D.92, G.248-G.251 G.252 G.253-G.255 A.54, A.56, G.256 H. Davenport CSAC 112/3/86 Index of correspondents RADO, Peter RADO, Richard RAMANUJAM, CC. P. RANKIN, Robert A. REDEI, L. REMAK, Robert RENDLE, A. RENYI, Alfred B REUTER, G. E. H. RICCI, Giovanni RICHERT, Hans-Egon RIDOUT, D. ROBERTS, Donald ROBINSON, G. de B. ROBINSON, Raphael M. ROBSON, R. ROGERS, Claude Ambrose ROGERS, Kenneth ROMANOFF, N. ROSEN, David ROTH, Klaus Friedrich ROUGHTON, Francis John Worsley ROYAL SOCIETY RUMNEY, Max RUSHTON, William Albert Hugh SADLER, Cyril SADLER, Donald H. SAELMAN,B. SALIE, Hans 139 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 E.132, G.265 A.65 G.266 D.164, G.267 A.85 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.281 A.85 G.282, G.283 A.49 A.68, D.201: G.284 A.71 A.49 A.86, G.285 G .286 G .287 H. Davenport CSAC 112/3/86 Index of correspondents 140 SAMET, Paul SAWYER, Desmond B. SCHERK, Peter SCHINZEL, Andrzej SCHMID, H. L. SCHMIDT, F. K. SCHMIDT, Wolfgang M. SCHNEIDER, Theodor SCHNITZER, Franz J. SCHOENFELD, Lowell SCHWARZ, Stefan SEMPLE, J. G. SHAW,Frank SHOVELTON, Sydney Taverner SIEGEL, Carl Ludwig SIERPINSKI, Waclaw SMITH, Cedric A. B. SMITHIES, Frank SPENCER, D.C. SPRENGER, E. SPRINDZUK, V. SRINIVASAN, B. G. R. STARK, Harold STEEN, S. W. P. STEWARD, G. C. STOLLER, Gerald STOPFORD, John Sebastian Bach, Baron SWINNERTON-DYER, Sir (Henry) Peter (Francis) SZEGO, Gabor SZEKERES, G. SZELE, Tibor A. 66 G.288 G.289 A.86, D.164, G.290 G.291 G.292 A.85 A.86 A.86, G.295 G .296 See also D.90 G.297 A.57, A.66 F Y 66 Y P A .60, A.66, G.188, G.189, .254, G.298 Y A F F .86, C.108, G.276, G.299- . 303 .86, G.304 66, G.305 - 66 .307 308 .309 .310 31] .66, G.136, G.312 r F a Q O a Q Q O Q M Q > A.66, G.313 G.314 A.49, A.53, A.55 A.66, A.86, D.99, E.134, G.315 A.60, D.92, G.316 G.317 G.318 H. Davenport CSAC 112/3/86 Index of correspondents TATCHELL, J. B. 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. VALLANCE, L._ S. VAN DER CORPUT, Jan G. VAN DER CORPUT, Jeannet VAN DER POL, Balthazar VAN DER WAERDEN, B. L. VANDIVER, H. S. VARNAVIDES, P. - L. WALD, A. WALFISZ, Arnold WALMSLEY, Charles WARD, G. W. WARD, J. WATSON, George L. 14] A.66 C.52, G.136 A.49, A.66, G.319 A.66, A.87, G.188 A.4l G.152, G.320 A.7] A.66, A.87, G.136, G.321 G .322 G.323 G.323 G .324 G .325 G .326 D.92, G.327 G .327 G .328 G .328A G .329 A.87, D.60, G.330-G.334 D.55 G .335, G.336 See also G. 64 D.92 G .337 A.53 A.88, G.338-G. 344 H. Davenport CSAC 112/3/86 Index of correspondents 142 WATSON, George Neville WHITEHART, F._ E. WHITELEY, J. ON. WHYTE, L. L. WIGGLESWORTH, Laurence WILCOCK, Bruce WILLIAMS, W. Lloyd G. WINSTANLEY, Denys A. WONHAM, W. M. WREN, J. L. WRIGHT, Edward Maitland WRIGHTON, R. F. YOUNGS, J. W. T. ZEEMAN, Erik Christopher ZERVOS, Spiros P. ZULAUF, Achim ZYGMUND, Antoni G.345 G .346 G .347 G .348 A.88 A.88 G .349 A.33 G .350 A.88 A.66, A.88, G.351 G.277 G.352 G.353 G.354 G.355 G .356

# DAVENPORT, Harold

Published: 13 September, 2023 Author: admin