Catalogue description Catalogue of the papers and correspondence of HAROLD DAVENPORT FRS; (1907 - 1969)

LIST OF CONTENTS

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

SECTION E RESEARCH NOTES AND DRAFTS E.1 - E.135

SECTION F FACULTY OF MATHEMATICS, CAMBRIDGE F.1 - F.17

SECTION G CORRESPONDENCE G.1 - G.373

The collection, which is substantial, covers most aspects of Davenport's life and work. Less fully represented are his extensive travels for visits and conferences (which can sometimes only be deduced from a jotted heading on a lecture script) and his work for the London Mathematical Society. His contributions to his subject, as 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Section A (Biographical and personal) includes Davenport's own unpublished reminiscences and reflections on his life's work, made shortly before his death with the assistance of his wife and his colleague D.J. Lewis (A.8 - A.10).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 documentation 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. On a 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).

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 C and 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. Erdös, 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. Correspondence 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 correspondence and in the drafts for lectures and papers elsewhere in the collection.

Compiled by:

Jeannine Alton

Peter Harper

Margaret Erskine

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

ACKNOWLEDGEMENTS

We are especially grateful to Mrs. Anne Davenport for her initial work in assembling the material and making it available, for invaluable provision of notes and information, for her instant recall of names, facts or handwriting, and for her unfailing help and encouragement throughout the compilation of this catalogue.

We gratefully acknowledge the help of Professor B.J. Birch in providing information and identifying documents, and in making available his own collaborative correspondence with Davenport as well as material on posthumous publications and the Royal Society Memoir.

Davenport, Harold, 1907-1969, scientist and mathematician

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.

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.

BIBLIOGRAPHY

Reproduced with permission from Biographical Memoirs of Fellows of the Royal Society, 17, 1971, 187-192.

(1) 1931. On the distribution of quadratic residues (mod p). J. Lond. Math. Soc. 6, 49-54.

(2) 1931. On Dirichlet's L-functions. J. Lond. Math. Soc. 6, 198-202.

(3) 1932. On the distribution of the power residues (mod p). J. Lond. Math. Soc. 7, 117-121.

(4) 1932. On a generalization of Euler's function [theta](n). J. Lond. Math. Soc. 7, 290-296.

(5) 1933. On certain exponential sums. J. für. Math. 169, 158-176.

(6) 1933. On the distribution of quadratic residues (mod p) (second paper). J. Lond. Math. Soc. 8, 46-52.

(7) 1933. Über numeri abundantes. Sitzungsber. Preuss. Akad. Wiss. Berlin, pp. 830-837.

(8) 1934. (With H. HASSE.) Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen. J. für Math. 172, 151-182.

(9) 1935. On the addition of residue classes. J. Lond. Math. Soc. 10, 30-32.

(10) 1935. Note on mean value theorems for the Reimann Zeta-function. J. Lond. Math. Soc. 10, 136-138.

(11) 1936. (With H. HEILBRONN.) On Warning's problem for fourth powers. Proc. Lond. Math. Soc. (2), 41, 143-150.

(12) 1936. (With H. HEILBRONN.) On the zeros of certain Dirichlet series. J. Lond. Math. Soc. 11, 181-185.

(13) 1936. The meromorphisms of an elliptic function-field. Proc. Camb. Phil. Soc. 32, 212-215.

(14) 1936. (With H. HEILBRONN.) On an exponential sum. Proc. Lond. Math. Soc. (2), 41, 449-453.

(15) 1936. (With H. HEILBRONN.) On the zeros of certain Dirichlet series (second paper). J. Lond. Math. Soc. 11, 307-312.

(16) 1936. (With P. ERDO^vS.) On sequences of positive integers. Acta Arithmetica, 2, 147-151.

(17) 1937. On some infinite series involving arithmetical functions. Quart. J. Math. 8, 8-13.

(18) 1937. (With H. HEILBRONN.) On Waring's problem: Two cubes and one square. Proc. Lond. Math. Soc. (2), 43, 73-104.

(19) 1937. (With H. HEILBRONN.) Note on a result in the additive theory of numbers. Proc. Lond. Math. Soc. (2), 43, 142-151.

(20) 1937. On primitive roots in finite fields. Quart. J. Math. 8, 308-312.

(21) 1937. On some infinite series involving arithmetical functions (II). Quart. J. Math. 8, 313-320.

(22) 1937. Note on a result of Siegel. Acta Arithmetica, 2, 262-265.

(23) 1938. Note on an identity connected with Diophantine approximation. Proc. Camb. Phil. Soc. 34, 27.

(24) 1938. On the product of three homogeneous linear forms. J. Lond. Math. Soc. 13, 139-145.

(25) 1938. On the product of three homogeneous linear forms (II). Proc. Lond. Math. Soc. (2), 45, 412-431.

(26) 1939. On the product of three homogeneous linear forms (III). Proc. Lond. Math. Soc. (2), 45, 98-125.

(27) 1939. Character sums in finite fields. Acta Mathematica, 71, 91-121.

(28) 1939. Minkowski's inequality for the minima associated with a convex body. Quart. J. Math. 10, 119-121.

(29) 1939. A simple proof of Remak's theorem on the product of three linear forms. J. Lond. Math. Soc. 14, 47-51.

(30) 1938. Sur les sommes de puissances entières. C.R. hebd. Acad. Sci. Paris, 207, 1366-1368.

(31) 1939. On sums of positive integral kth powers. Proc. Royal. Soc. Lond. A, 170, 293-299.

(32) 1940. On linear fractional substitutions with large determinant. Annals of Math. 41, 59-62.

(33) 1939. On Waring's problem for cubes. Acta Math. 71, 123-143.

(34) 1942. On sums of positive integral kth powers. Amer. J. Math. 64, 189-198.

(35) 1939. On Waring's problem for fourth powers. Annals of Math. 40, 731-747.

(36) 1939. (With P. ERDÕS.) On sums of positive integral kth powers. Annals of Math. 40, 533-536.

(37) 1942. On Waring's problem for fifth and sixth powers. Amer. J. Math. 64, 199-207.

(38) 1941. Note on sums of fourth powers. J. Lond. Math. Soc. 16, 3-4.

(39) 1941. Note on the product of three homogeneous linear forms. J. Lond. Math. Soc. 16, 98-101.

(40) 1941. On a conjecture of Mordell. Proc. Camb. Phil. Soc. 37, 325-330.

(41) 1943. On the minimum of a binary cubic form. J. Lond. Math. Soc. 18, 168-176.

(42) 1943. On the product of three homogeneous linear forms (IV). Proc. Camb. Phil. Soc. 39, 1-21.

(43) 1944. On the minimum of a ternary cubic form. J. Lond. Math. Soc. 19, 13-18.

(44) 1946. On the minimum of X + Y +Z. J. Lond. Math. Soc. 21, 82-86.

(45) 1945. On the reduction of a binary cubic form (I) J. Lond. Math. Soc. 20, 14-22.

(46) 1945. On the reduction of a binary cubic form (II). J. Lond. Math. Soc. 20, 139-147.

(47) 1946. (With K. MAHLER.) On simultaneous Diophantine approx mation. Duke Math. J. 13, 105-111.

(48) 1946. On a theorem of Tschebotareff. J. Lond. Math. Soc. 21, 28-34; and 24 (1949), 316.

(49) 1946. (With H. HEILBRONN.) On indefinite quadratic forms in five variables. J. Lond. Math. Soc. 21, 185-193.

(50) 1946. On the product of n homogeneous linear forms. Proc. K. Ned. Akad. van Wet. Amsterdam, 49, 822-828.

(51) 1946. Non-homogeneous binary quadratic forms. Proc. K. Ned. Akad. van Wet. Amsterdam, 49, 815-821.

(52) 1947. On the product of three non-homogeneous linear forms. Proc. Camb. Phil. Soc. 43, 137-152.

(53) 1946. (With J. G. VAN DER CORPUT.) On Minkowski's fundamental theorem in the geometry of numbers. Proc. K. Ned. Akad. van Wet. Amsterdam, 49, 701-707.

(54) 1947. (With H. HEILBRONN.) On the minimum of a bilinear form. Quart. J. Math. 18, 107-121.

(55) 1947. (With H. HEILBRONN.) Asymmetric inequalities for non-homogeneous linear forms. J. Lond. Math. Soc. 22, 53-61.

(56) 1949. On indefinite ternary quadratic forms. Proc. Lond. Math. Soc. (2), 51, 145-160.

(57) 1947. On a theorem of Markoff. J. Lond. Math. Soc. 22, 96-99.

(58) 1947. (With C. A. ROGERS.) Hlawka's theorem in the geometry of numbers. Duke Math. J. 14, 367-374.

(59) 1947. The geometry of numbers. Nature, Lond. 159, 104.

(60) 1947. A historical note. J. Lond. Math. Soc. 22, 100-101.

(61) 1947. Non-homogeneous binary quadratic forms (II). Proc. K. Ned. Akad. van Wet. Amsterdam, 50, 378-389.

(62) 1947. Non-homogeneous binary quadratic forms (III). Proc. K. Ned. Akad. van Wet. Amsterdam, 50, 484-491.

(63) 1948. Non-homogeneous ternary quadratic forms. Acta Math. 80, 65-95.

(64) 1947. Sur une extension d'un théorème de Minkowski. C.R. hebd. Acad. Sci. Paris, 224, 990-991.

(65) 1946. W. E. H. Berwick. Obituary notice. J. Lond. Math. Soc. 21, 74-80.

(66) 1947. Non-homogeneous binary quadratic forms (IV). Proc. K. Ned. Akad. van Wet. Amsterdam, 50, 741-749, 909-917.

(67) 1947. The geometry of numbers (lecture given to the Math. Assoc. 9 April 1947). Math. Gaz. 31, 206-210.

(68) 1950. On a theorem of Khinchine. Proc. Lond. Math. Soc. (2), 52, 65-80.

(69) 1949. (With G. PÓLYA.) On the product of two power series. Canad. J. Math. 1, 1-5.

(70) 1950. Indefinite binary quadratic forms, and Euclid's algorithm in real quadratic fields. Proc. Lond. Math. Soc. (2), 53, 65-82.

(71) 1948. Note on indefinite ternary quadratic forms. J. Lond. Math. Soc. 23, 199-202.

(72) 1948. (With MARSHALL HALL.) On the equation ax² + y² + cz² = 0. Quart. J. Math. 19, 189-192.

(73) 1949. A divisor problem. Quart. J. Math. 20, 37-44.

(74) 1950. (With H. CHATLAND.) Euclid's algorithm in real quadratic fields. Canad. J. Math. 2, 289-296.

(75) 1949. Sur les corps cubiques à discriminants négatifs. C.R. hebd. Acad. Sci. Paris, 228, 883-885.

(76) 1950. Euclid's algorithm in cubic fields of negative discriminant. Acta Math. 84, 159-179.

(77) 1950. Indefinite binary quadratic forms. Quart. J. Math. (2), 1, 54-62.

(78) 1949. On the series for L(1). J. Lond. Math. Soc. 24, 229-233.

(79) 1950. (With C. A. ROGERS.) Diophantine inequalities with an infinity of solutions. Phil. Trans. Roy. Soc. Lond. A, 242, 311-344.

(80) 1949. (With C. A. ROGERS.) A note on the geometry of numbers. J. Lond. Math. Soc. 24, 271-280.

(81) 1950. (With C. A. ROGERS.) On the critical determinants of cylinders. Quart. J. Math. (2), 1, 215-218.

(82) 1950. Euclid's algorithm in certain quartic fields. Trans. Amer. Math. Soc. 68, 508-532.

(83) 1950. Note on a binary quartic form. Quart. J. Math. (2), 1, 253-261.

(84) 1950. L'algorithme d'Euclide dans certains corps algébriques. Colloques Internat. du C.N.R.S. Paris, 24, 41-43.

(85) 1950. Study and research in mathematics. Math. Gaz. 34, 161-165.

(86) 1950. Waring's problem (contribution to the obituary notice of G. H. Hardy). J. Lond. Math. Soc. 25, 119-125.

(87) 1950. Sums of three positive cubes. J. Lond. Math. Soc. 25, 339-343.

(88) 1951. Note on a principle of Lipschitz. J. Lond. Math. Soc. 26, 179-183.

(89) 1951. On the class-number of binary cubic forms (I). J. Lond. Math. Soc. 26, 183-192; 27 (1952), 512.

(90) 1951. On the class-number of binary cubic forms (II). J. Lond. Math. Soc. 26, 192-198.

(91) 1950. Recent progress in the geometry of numbers. Proc. Internat. Congress of Math. Harvard, 1, 166-174.

(92) 1951. (With P. ERDÖS.) On sequences of positive integers. J. Indian Math. Soc. 15, 19-24.

(93) 1952. (With P. ERDÖS.) On normal decimals. Canad. J. Math. 4, 58-63.

(94) 1952. Linear forms associated with an algebraic number-field. Quart. J. Math. (2), 3, 32-41.

(95) 1952. Note on a result of Chalk. Quart. J. Math. (2), 3, 130-138.

(96) 1951. Prime numbers. Scientific Journal of the Royal College of Science, 21, 1-9.

(97) 1952. (With R. P. BAMBAH.) The covering of n-dimensional space by spheres. J. Lond. Math. Soc. 27, 224-229.

(98) 1951. Sur un système de sphères qui recouvrent l'espace à n-dimensions. C.R. hebd. Acad. Sci. Paris, 233, 571-573.

(99) 1952. The covering of space by spheres. Rend. Circolo Mat. di Palermo, Serie II, 1, 92-107.

(100) 1952. Simultaneous Diophantine approximation. Proc. Lond. Math. Soc. (3), 2, 406-416.

(101) 1952. (With P. ERDÕS.) The distribution of quadratic and higher residues. Publicationes Math. (Debrecen), 2, 252-265.

(102) 1953. On the product of n-linear forms. Proc. Camb. Phil. Soc. 49, 190-193.

(103) 1954. (With G. L. WATSON.) The minimal points of a positive definite quadratic form. Mathematika, 1, 14-17.

(104) 1954. Simultaneous Diophantine approximation. Mathematika, 1, 51-72.

(105) 1955. On a theorem of Furtwängler. J. Lond. Math. Soc. 30, 186-195.

(106) 1954. Simultaneous Diophantine approximation. Proc. Internat. Congress of Math. Amsterdam, III, 9-12.

(107) 1955. (With H. P. F. SWINNERTON-DYER.) Products of inhomogeneous linear forms. Proc. Lond. Math. Soc. (3), 5, 474-499.

(108) 1955. (With K. F. ROTH.) The solubility of certain Diophantine inequalities. Mathematika, 2, 81-96.

(109) 1955. (With K. F. ROTH.) Rational approximations to algebraic numbers. Mathematika, 2, 160-167.

(110) 1955. Le recouvrement de l'espace par des sphères. Colloque sur la thèorie des nombres (Centre Belge des Recherches Mathématiques), pp. 139-145.

(111) 1957. Note on a theorem of Cassels. Proc. Camb. Phil. Soc. 53, 539-540.

(112) 1956. Indefinite quadratic forms in many variables. Mathematika, 3, 81-101.

(113) 1956. Note on irregularities of distribution. Mathematika, 3, 131-135.

(114) 1958. Indefinite quadratic forms in many variables II. Proc. Lond. Math. Soc. (3), 8, 109-126.

(115) 1958. (With B. J. BIRCH.) Quadratic equations in several variables. Proc. Camb. Phil. Soc. 54, 135-138.

(116) 1959. Cubic forms in 32 variables. Phil. Trans. Royal Soc. Lond. A, 251, 193-232.

(117) 1958. T. Vijayaraghavan. Obituary notice in J. Lond. Math. Soc. 33, 252-255.

(118) 1958. (With B. J. BIRCH.) Indefinite quadratic forms in many variables. Mathematika, 5, 8-12.

(119) 1958. (With B. J. BIRCH.) On a theorem of Davenport and Heilbronn. Acta. Math. 100, 259-279.

(120) 1959. (With D. RIDOUT.) Indefinite quadratic forms. Proc. Lond. Math. Soc. (3), 9, 544-555.

(121) 1958. The work of Dr K. F. Roth. Proc. Internat. Congress of Mathematicians, Edinburgh, pp. lvii-lx.

(122) 1959. Dirichlet. Math. Gaz. 43, 268-269.

(123) 1960. Some recent progress in analytic number theory. J. Lond. Math. Soc. 35, 135-142.

(124) 1961. (With S. CHOWLA.) On Weyl's inequality and Waring's problem for cubes. Acta Arithmetica, 6, 505-521.

(125) 1960. On a theorem of P. J. Cohen. Mathematika, 7, 93-97.

(126) 1961. A note on binary cubic forms. Mathematika, 8, 58-62.

(127) 1960. Über einige neuere Fortschritte der additiven Zahlentheorie. Jber. Deutsch. Math. Vereinigung, 63, 163-169.

(128) 1962. (With B. J. BIRCH.) Note on Weyl's inequality. Acta Arithmetica, 7, 273-277.

(129) 1961. (With D. J. LEWIS & A. SCHINZEL.) Equations of the form f(x) = g(y). Quart. J. Math. (2), 12, 304-312.

(130) 1962. Cubic forms in 29 variables. Proc. Royal Soc. London. A, 266, 287-298.

(131) 1962. (With B. J. BIRCH & D. J. LEWIS.) The addition of norm forms. Mathematika, 9, 75-82.

(132) 1961. A. E. Western. Obituary notice. Nature, Lond. 192, 1022.

(133) 1962. A note on Diophantine approximation. Studies in Mathematical Analysis and related topics. Stanford University Press, pp. 77-81.

(134) 1963. Cubic forms in 16 variables. Proc. Royal Soc. Lond. A, 272, 285-303.

(135) 1962. (With D. J. LEWIS.) Exponential sums in many variables. Amer. J. Math. 84, 649-665.

(136) 1963. (With D. J. LEWIS.) Notes on congruences (I). Quart. J. Math. (2), 14, 51-60.

(137) 1963. (With D. J. LEWIS.) Notes on congruences (II). Quart. J. Math. (2), 14, 153-159.

(138) 1963. (With D. J. LEWIS.) Homogeneous additive equations. Proc. Royal Soc. Lond. A, 274, 443-460.

(139) 1963. (With D. J. LEWIS.) An analogue of a problem of Littlewood. Michigan Math. J. 10, 157-160.

(140) 1963. A problematic identity. Mathematika, 10, 10-12.

(141) 1963. (With D. J. LEWIS.) Primitive roots in finite fields. Rend. Circolo Mat. Palermo, 12, 129-136.

(142) 1963. (With P. ERDÕS & W. J. LE VEQUE.) On Weyl's criterion for uniform distribution. Michigan Math. J. 10, 311-314.

(143) 1963. (With W. J. LE VEQUE.) Uniform distribution relative to a fixed sequence. Michigan Math. J. 10, 315-319.

(144) 1964. A note on Diophantine approximation (II). Mathematika, 11, 50-58.

(145) 1964. (With D. J. LEWIS & A. SCHINZEL.) Polynomials of certain special types. Acta Arithmetica, 9, 107-116.

(146) 1964. (With A. SCHINZEL.) Two problems concerning polynomials. Journal für Math. 214-215, 386-391; and corrigendum, 218 (1965), 220.

(147) 1963. (With P. ERDÕS.) A theorem on uniform distribution. Publ. Math. Inst. Hungarian Acad. Sci. A, 8, 3-11.

(148) 1964. (With D. J. LEWIS.) Non-homogeneous cubic equations. J. Lond. Math. Soc. 39, 657-671.

(149) 1964. L. J. Mordell. Acta Arithmetica, 9, 2-12.

(149a) 1964. Publications of L. J. Mordell. Acta Arithmetica, 9, 13-22.

(150) 1966. (With E. BOMBIERI.) On two problems of Mordell. Amer. J. Math. 88, 61-70.

(151) 1964. A remark on continued fractions. Michigan Math. J. 11, 343-344.

(152) 1965. (With A. SCHINZEL.) A note on sequences and subsequences. Elemente der Math. 20, 63-64.

(153) 1965. On a theorem of Mrs. Turán. Proc. Lond. Math. Soc. (3), 14A, 76-80.

(154) 1965. (With A. SCHINZEL.) A combinatorial problem connected with differential equations. Amer. J. Math. 87, 684-694.

(155) 1966. Note on an irrational power series. Proc. Amer. Math. Soc. 17, 1-5.

(156) 1964. Corrigendum. Note on a principle of Lipschitz. J. Lond. Math. Soc. 39, 580.

(157) 1966. On a theorem of Mrs Turán. II. Proc. Lond. Math. Soc. (3), 16, 570-576.

(158) 1966. (With D. J. LEWIS & A. SCHINZEL.) Quadratic Diophantine equations with a parameter. Acta Arithmetica, 11, 353-358.

(159) 1965. On f (t)-g(t). K. Norske Vid. Selskabs Forh. 38, 86-87.

(160) 1965. Problems of packing and covering. Rend. Sem. Mat. Univ. e Polytec. di Torino, 24, 41-48.

(161) 1965. The London Mathematical Society. Nature, Lond. 207, 350-351.

(162) 1966. Looking back. J. Lond. Math. Soc. 41, 1-10.

(163) 1966. (With E. BOMBIERI.) Small differences between prime numbers. Proc. Royal Soc. Lond. A, 293, 1-18.

(164) 1965. Quelques problèmes d'approximation diophantienne. Rend. Sem. Mat. Milano, 35, 3-8.

(165) 1966. (With A. SCHINZEL.) A note on certain arithmetical constants. Illinois J. Math. 10, 181-185.

(166) 1967. (With A. SCHINZEL.) Diophantine approximation and sums of roots of unity. Math. Annalen, 169, 118-135.

(167) 1966. (With D. J. LEWIS.) Cubic equations of additive type. Phil. Trans. Royal Soc. Lond. A, 261, 97-136.

(168) 1966. (With H. HALBERSTAM.) The value of a trigonometrical polynomial at well spaced points. Mathematika, 13, 91-96.

(169) 1966. (With D. J. LEWIS.) Notes on congruences III. Quart. J. Math. 17, 339-344.

(170) 1966. (With H. HALBERSTAM.) Primes in arithmetic progressions. Michigan Math. J. 13, 485-489.

(171) 1966. Eine Bemerkung über Dirichlets L.Funktionen. Göttinger Nachrichten, pp. 203-212.

(172) 1968. (With E. BOMBIERI.) On the large sieve method. Abhandlungen aus Zahlentheorie u. Anal. Zur Erinnerung an Edmund Landau (1877-1938). Berlin: VEB Deutsch. Verlag d. Wiss. pp. 11-12.

(173) 1967. (With W. M. SCHMIDT.) Approximation to real numbers by quadratic irrationals. Acta Arithmetica, 13, 169-176.

(174) 1968. (With E. LANDAU.) On the representation of positive integers as sums of three cubes of positive rational numbers, Abhandlungenaus Zahlentheorie aus Anal. Zur Erinnerung an Edmund Landau (1877-1938). Berlin: VEB Deutsch. Verlag d. Wiss. pp. 51-53.

(175) 1968. Bases for finite fields. J. Lond. Math. Soc. 43, 21-39.

(176) 1967. On a theorem of Heilbronn. Quart. J. of Math. 18, 339-344.

(177) 1968. (With W. M. SCHMIDT.) A theorem on linear forms. Acta Arithmetica, 14, 209-223.

(178) 1967. A. E. Ingham. Nature, Lond. 216, 311.

(179) 1967. (With H. HALBERSTAM.) Corrigendum and addendum. Mathematika, 14, 229-232.

(180) 1968. A note on Thue's theorem. Mathematika, 15, 76-87.

(181) 1969. (With E. BOMBIERI.) Some inequalities involving trigonometrical polynomials. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. 23 (Fasc. 2), 223-241.

(182) 1969. (With E. BAKER.) The equations 3x²-2 = y² and 8x²-7 = z². Quart. J. Math. (2), 20, 129-137.

(183) 1969. (With W. M. SCHMIDT.) Approximation to real numbers by algebraic integers. Acta Arithmetica, 15, 393-416.

(184) 1969. (With D. J. LEWIS.) Simultaneous equations of additive type. Phil. Trans. Royal Soc. Lond. A, 264, 557-595.

(185) 1970. (With W. M. SCHMIDT.) Dirichlet's theorem on Diophantine approximation. Symposia mathematica, 4, Istituto Nazionale di alta Mathematica. London: Academic Press, pp. 113-132.

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(188) 1970. (With W. M. SCHMIDT.) Supplement to a theorem on linear forms. Colloquia Mathematica Societatis János Bolyai, 2. Number Theory. Debrecen, Hungary, 1968. Budapest and Amsterdam, pp. 15-25.

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• Mathematics

OUTLINE OF THE CAREER OF HAROLD DAVENPORT

Davenport was born and educated in Accrington, where his gifts for mathematics and chemistry were early recognised. At the age of sixteen he was awarded scholarships to attend Manchester University (1924 - 27) winning first-class honours and the respect of such tutors as L.J. Mordell and E.A. Milne. The latter encouraged him to enter for a scholarship at Trinity College Cambridge, where he read for the Tripos (1927 - 29), began research with J.E. Littlewood, won a Rayleigh Prize (1931) and a Trinity Fellowship (1932 - 37). Another important event of this period was Davenport's acceptance of an invitation by H. Hasse to stay with him in Marburg, a visit which enabled Davenport to meet several distinguished German mathematicians and to learn the language thoroughly. His first university post was a return to Manchester as Assistant Lecturer (1937 - 41) and in 1941 he was appointed to his first Chair at University College of North Wales, Bangor. In 1945 Davenport, who had married Anne Lofthouse in 1944, moved to University College London as Astor Professor. His first American visit, to Stanford in 1947 - 48, occurred during the London period and was followed by many later transatlantic journeys of varying duration. It was also from the Mathematics Department of University College that Davenport launched the new journal Mathematika (1953). In 1958 he was elected Rouse Ball Professor of Mathematics and Fellow of Trinity College, Cambridge, where he died in 1969.

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