| Title |
SECTION D PUBLICATIONS |
| Reference |
D.1 - D.213 |
|
| Content and context |
| Davenport published nearly 200 papers, as well as three books. Most of the material in this Section consists of drafts of the published papers, frequently without any other material such as notes or calculations. In some cases however these do survive and in others there is more than one draft. Some correspondence is included here, for example, D.112 - D.116. The sequence incorporates material of other kinds, such as the Adams Prize Essay (D.5 - D.15), the books The higher arithmetic (D.89 - D 92) and Multiplicatative number theory (D.170 - D.182), reviews by Davenport (D.208), and some unpublished material, such as `On writing mathematical papers' (D.201 - D.203). Material published after Davenport's death can be found at D.204 - D.207, and his `collected works' are represented at D.210 - D.213. The material has been arranged in chronological order, and where applicable the Bibliography number of the Royal Society Memoir has been given, as well as the date of publication. |
| Further information |
| For additional correspondence and material exchanged with collaborators in publications, see the relevant entries in Section G and also E 1 - E 15 (work with H. Hasse). |
| Trinity/DAVT/D.1 - D.213 contains: |
|
D.1
|
`On certain exponential sums'. (Bibliog. 5). 19pp. typescript draft (incomplete), with ms. corrections; 4pp. typescript draft. |
1933 |
|
D 2
|
`On the product of three linear homogeneous forms (II)'. (Bibliog.25). 31pp. typescript draft with ms. corrections; 1p. ms. calculations. |
1938 |
|
D.3
|
`On the product of three homogeneous linear forms (III)'. (Bibliog. 26). 37pp. typescript draft with ms. corrections. |
1939 |
|
D.4
|
`On Waring's problem for fourth powers'. (Bibliog. 35). 30pp. ms. draft. |
1939 |
|
D.5-D.15
|
Adams Prize Essay for 1939-40. |
|
|
D.16
|
`On sums of positive integral Kth powers' with P. Erdös. (Bibliog. 36). 4pp. ms. draft (Erdös's hand). |
1939 |
|
D.17
|
`On linear fractional substitutions with large determinant'. (Bibliog. 32). 6pp. ms. draft. |
1940 |
|
D.18
|
`Note on the product of three homogeneous linear forms'. (Bibliog. 39). 4pp. ms. draft. |
1941 |
|
D.19
|
`On a conjecture of Mordell concerning binary cubic forms'. (Bibliog. 40). 12pp. typescript and ms. draft. |
1941 |
|
D.20
|
`On sums of positive integral kth powers'. (Bibliog. 34). 4pp. ms. notes. |
1942 |
|
D.21
|
`On sums of positive integral Kth powers'. (Bibliog. 34). 18pp. ms. draft. |
1942 |
|
D.22
|
`On sums of positive integral kth powers'. (Bibliog. 34). 6pp. galley-proof, with ms. corrections. |
1942 |
|
D.23
|
`On Waring's problem for fifth and sixth powers'. (Bibliog. 37). 14pp. ms. draft. |
1942 |
|
D.24
|
`On the minimum of a binary cubic form'. (Bibliog. 41). 4 ms. drafts, 6pp., 7pp., 10pp. and 11pp. |
1943 |
|
D.25
|
`On the minimum of a binary cubic form'. (Bibliog. 41). 1p. ms. calculations, 14pp. typescript draft. |
1943 |
|
D.26
|
`On the product of three homogeneous linear forms (IV)'. (Bibliog. 42). Ms. draft paginated 1-45 (p.24 missing). |
1943 |
|
D.27
|
`On the product of three homogeneous linear forms (IV)'. (Bibliog. 42). 32pp. ms. draft. |
1943 |
|
D.28
|
`On the minimum of a ternary cubic form'. (Bibliog. 43). 10pp. ms. draft. |
1944 |
|
D.29
|
`The reduction of a binary cubic form (I)'. (Bibliog. 45). 8pp. typescript draft with ms. corrections. |
1945 |
|
D.30
|
`The reduction of a binary cubic form (II)'. (Bibliog. 46). 12pp. ms. draft; 8pp. typescript draft with ms. corrections. |
1945 |
|
D.31
|
`On the minimum of x³ y³ z³'. (Bibliog. 44). 2 ms. drafts, 5pp. and 6pp. |
1946 |
|
D.32
|
`Simultaneous Diophantine approximation', with K. Mahler. (Bibliog. 47). 8pp. ms. draft; 6pp. typescript draft. |
1946 |
|
D.33
|
`On a theorem of Tschebotareff'. (Bibliog. 48). 2 ms. drafts, each 7pp. |
1946 |
|
D.34
|
`On indefinite quadratic forms in five variables', with H. Heilbronn. (Bibliog. 49). 12pp. ms. draft (Heilbronn's hand); 9pp. ms. draft. |
1946 |
|
D.35
|
`The product of n homogeneous linear forms'. (Bibliog. 50). 8pp. ms. draft. |
1946 |
|
D.36
|
`Non-homogeneous binary quadratic forms'. (Bibliog. 51). 7pp. and 8pp. ms. drafts. |
1946 |
|
D.37
|
Publications. `Theory of Numbers', 1946-47. Davenport was approached, initially by E.A. Milne, to write a book on this subject as one of a series of mathematical works for the interested layman. The book was published in 1952 as `The higher arithmetic'. 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. |
1946–1947 |
|
D.38
|
`On the product of three non-homogeneous linear forms'. (Bibliog. 52). 20pp. typescript draft, with ms. corrections. |
1947 |
|
D.39
|
`Asymmetric inequalities for non-homogeneous linear forms', with H. Heilbronn. (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. |
1947 |
|
D.40
|
`On a theorem of Markoff'. (Bibliog. 57). 5pp. ms. draft. |
1947 |
|
D.41
|
`On Hlawka's theorem in the geometry of numbers', with C.A. Rogers. (Bibliog. 58). Postcard from Rogers, 3 January 1947, re solution to an equation, and 3pp. ms. notes; 11pp. ms. draft, 1p. labelled `Prelim to 58'; 10pp. ms. `final' draft. |
1947 |
|
D.42
|
`The Geometry of Numbers'. (Bibliog. 59). 4pp. typescript draft. |
1947 |
|
D.43
|
`A historical note'. (Bibliog. 60). 2pp. typescript draft with ms. corrections. |
1947 |
|
D.44
|
`Non-homogeneous binary quadratic forms II'. (Bibliog. 61). 14pp. typescript draft with ms. corrections. |
1947 |
|
D.45
|
`Non-homogeneous binary quadratic forms III'. (Bibliog. 62). 9pp. typescript draft. |
1947 |
|
D.46
|
`Sur une extension d'un théorème de Minkowski'. (Bibliog. 64). 2pp. ms. draft. |
1947 |
|
D.47
|
`Non-homogeneous binary quadratic forms IV'. (Bibliog 66). 11pp. ms. notes and calculations, 1p. labelled `Prelim to 66'. |
1947 |
|
D.48
|
`Non-homogeneous binary quadratic forms IV'. (Bibliog 66). 24pp. ms. draft. |
1947 |
|
D.49
|
Publications`The geometry of numbers'. (Bibliog. 67). 10pp. typescript draft. |
1947 |
|
D.50
|
`Non-homogeneous ternary quadratic forms'. (Bibliog. 63). 34pp. ms. draft. |
1948 |
|
D.51
|
`Note on indefinite ternary quadratic forms'. (Bibliog. 71). 4pp. typescript draft with ms. corrections. |
1948 |
|
D.52
|
`On the equation ax² by² cz² =O'. (Bibliog. 72). 5pp. typescript draft with ms. corrections, with 1p. ms. addition. |
1948 |
|
D.53
|
`On indefinite ternary quadratic forms'. (Bibliog. 56). 14pp. typescript draft with ms. corrections, with 1p. ms. addition. |
1949 |
|
D 54
|
`On the product of two power series', with G. Pólya. (Bibliog. 69). 9pp. typescript draft; 10pp. ms. and typescript draft. |
1949 |
|
D.55
|
`On a result of Wald', with G. Pólya. (Unpublished). 2 ms. drafts, 6pp. and 5pp.; letter from Wald, 19 September 1949, to Pólya. |
1949 |
|
D.56
|
`A divisor problem'. (Bibliog. 73). 11pp. ms. draft. |
1949 |
|
D.57
|
`On the series for L(1)'. (Bibliog. 73). 5pp. typescript draft with ms. corrections. |
1949 |
|
D.58
|
`On a theorem of Khintchine'. (Bibliog. 68). 18pp. typescript draft with ms. corrections. |
1950 |
|
D.59
|
`Indefinite binary quadratic forms, and Euclid's algorithm in real quadratic fields'. (Bibliog.70). 25pp. typescript draft with ms. corrections. |
1950 |
|
D.60-D.62
|
`Euclid's algorithm in real quadratic fields', with H. Chatland, 1950 (Bibliog. 74). |
|
|
D.63
|
`Euclid's algorithm in cubic fields of negative discriminant'. (Bibliog. 76). 23pp. typescript draft with ms. corrections, with 7pp. ms. additions. |
1950 |
|
D.64
|
`Indefinite binary quadratic forms'. (Bibliog. 77). 13pp. ms. draft, labelled `prelim to 77'. |
1950 |
|
D.65
|
`Indefinite binary quadratic forms'. (Bibliog. 77). 11pp. and 6pp. ms. drafts, both labelled `prelim to 77'. |
1950 |
|
D.66
|
`Indefinite binary quadratic forms'. (Bibliog. 77). 12pp. typescript draft with ms. corrections, with note from editor, T.W. Chaundy, re corrections. |
1950 |
|
D.67
|
`Diophantine inequalities with an infinity of solutions', with C.A. Rogers. (Bibliog. 79). 59pp. typescript draft with ms. corrections; 1p. ms. list of contents. |
1950 |
|
D.68
|
`On the critical determinants of cylinders', with C.A. Rogers. (Bibliog. 81). 5pp. typescript draft with ms. corrections. |
1950 |
|
D.69
|
`Euclid's algorithm in certain quartic fields'. (Bibliog. 82). 34pp. typescript draft with ms. corrections. |
1950 |
|
D.70
|
`Note on a binary quartic form'. (Bibliog. 83). 10pp. typescript draft with ms. corrections. |
1950 |
|
D.71
|
`L'algorithme d'Euclide dans certains corps algébriques'. (Bibliog. 84). 7pp. typescript draft, in English, labelled `basis of lecture of Paris congress Sept 1949'; 9pp. ms. draft (in French). |
1950 |
|
D.72
|
`Study and Research in Mathematics'. (Bibliog. 85). 9pp. typescript draft. |
1950 |
|
D.73
|
`Sums of three positive cubes'. (Bibliog. 87). 6pp. ms. draft; 7pp. typescript draft. |
1950 |
|
D.74
|
`Recent progress in the geometry of numbers'. (Bibliog. 91). 5pp. ms. draft with 3pp. ms. notes; 15pp. ms. draft labelled `Second draft (used at lecture)' and `Congress lecture'. |
1950 |
|
D.75
|
`Recent progress in the geometry of numbers'. (Bibliog. 91). 13pp. typescript draft with ms. corrections. |
1950 |
|
D.76
|
`On a principle of Lipschitz'. (Bibliog. 88). 5pp. typescript draft labelled `prelim to 88', with 4pp. ms. notes; 6pp. typescript draft. |
1951 |
|
D.77
|
`On the class-number of binary cubic forms (I)'. (Bibliog. 89). 8pp. typescript draft, entitled `On binary cubic forms', labelled `preliminary to 89'; 11pp. typescript draft. |
1951 |
|
D.78
|
`On the class-number of binary cubic forms (II)'. (Bibliog. 90). 7pp. typescript draft. |
1951 |
|
D.79
|
`On sequences of positive integers', with P. Erdös. (Bibliog. 92). 6pp. typescript and ms. draft. |
1951 |
|
D.80
|
`Prime Numbers'. (Bibliog. 96). 10pp. typescript draft with ms. corrections. |
1951 |
|
D.81
|
`Sur un système de sphères qui recouvrent I'espace à n dimensions'. (Bibliog. 98). 4pp. 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). |
1951 |
|
D.82
|
`Note on normal decimals', with P. Erdös. (Bibliog. 93). 8pp. photocopy of typescript draft. |
1952 |
|
D.83
|
`Linear forms associated with an algebraic number-field'. (Bibliog. 94). 15pp. ms. and typescript draft. |
1952 |
|
D.84
|
`Note on a resuzlt of Chalk'. (Bibliog. 95). 12pp. photocopy of typescript draft. |
1952 |
|
D.85
|
`The covering of n dimensional space by spheres', with R.P. Bambah. (Bibliog. 97). 7pp. ms. and typescript draft. |
1952 |
|
D.86
|
`The covering of space by spheres'. (Bibliog. 99). 20pp. typescript draft. |
1952 |
|
D.87
|
`Simultaneous Diophantine approximation'. (Bibliog. 100). 15pp. typescript draft with ms. corrections. |
1952 |
|
D.88
|
`The distribution of quadratic and higher residues', with P. Erdös. (Bibliog. 101). 16pp. photocopy of typescript draft. |
1952 |
|
D.89-D.92
|
`The Higher Arithmetic', 1952 See also D.37. |
|
|
D.93
|
`The minimal points of a positive definite quadratic form', with G.L. Watson. (Bibliog. 103). 5pp. typescript draft with ms. corrections. |
1954 |
|
D.94
|
`Simultaneous Diophantine approximation'. (Bibliog. 104). 34pp. typescript draft. |
1954 |
|
D.95
|
Mathematika, vol.1, part 1. Davenport was responsible for the founding of this journal (see Memoir, p.164), and remained an editor throughout his life. The first issue contained 2 papers by him (Bibliog. 103 and 104). Proof copy with Davenport's ms. corrections, including 1p. ms. notes. |
June 1954 |
|
D.96
|
`Simultaneous Diophantine approximation'. (Bibliog. 106). 5pp. typescript draft. |
1954 |
|
D.97
|
`On a theorem of Furtwängler'. (Bibliog. 105). 15pp. ms. draft. |
1955 |
|
D.98
|
`On a theorem of Furtwängler'. (Bibliog. 105). 19pp. typescript draft with ms. corrections. |
1955 |
|
D.99
|
`Products of inhomogeneous linear forms', with H.P.F. Swinnerton-Dyer. (Bibliog. 107). 2 letters from H.P.F. Swinnerton-Dyer, 1954, re publication 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. |
1955 |
|
D.100
|
`Products of inhomogeneous linear forms', with H.P.F. Swinnerton-Dyer. (Bibliog. 107). 33pp. untitled ms. draft (Swinnerton-Dyer's hand), labelled `first version'. |
1955 |
|
D.101
|
`Products of inhomogeneous linear forms', with H.P.F. Swinnerton-Dyer. (Bibliog. 107). 44pp. typescript draft with ms. corrections. |
1955 |
|
D.102
|
`The solubility of certain Diophantine inequalities', with K.F. Roth. (Bibliog. 108). 24pp. paginated draft. |
1955 |
|
D.103
|
`Rational approximations to algebraic numbers', with K.F. Roth. (Bibliog. 109). 15pp. typescript draft with ms. corrections. |
1955 |
|
D.104
|
`Le recouvrement de l'espace par des sphères'. (Bibliog. 110). 12pp. ms. draft. |
1955 |
|
D.105
|
`Indefinite quadratic forms in many variables'. (Bibliog. 112). 26pp. typescript draft with ms. corrections. |
1956 |
|
D.106
|
`Note on irregularities of distribution'. (Bibliog. 113). 8pp. ms. draft. |
1956 |
|
D.107
|
`Indefinite quadratic forms in many variables II'. (Bibliog. 114). 34pp. ms. draft. |
1958 |
|
D.108
|
`Indefinite quadratic forms in many variables II'. (Bibliog. 114). Proofs, with ms. corrections. |
1958 |
|
D.109
|
`Indefinite quadratic forms in many variables (III)', with B.J. Birch. (Bibliog. 118). 6pp. typescript draft, with ms. corrections by both authors. |
1958 |
|
D.110
|
`On a theorem of Davenport and Heilbronn', with B.J. Birch. (Bibliog. 119). 6pp. ms. draft (in Birch's hand), entitled `Davenport's version of "A theorem of Davenport & Heilbronn"'. 19pp. ms. draft (in Davenport's hand), labelled `superseded'. |
1958 |
|
D.111
|
`On a theorem of Davenport and Heilbronn', with B.J. Birch. (Bibliog. 119). 37pp. typescript draft with ms. corrections. |
1958 |
|
D.112-D.116
|
Correspondence with B.J. Birch, re joint papers. |
June 1957-July 1958 |
|
D.117-D.120
|
Notes and drafts found with D.109-D.116, probably related to Bibliog. 118 and 119. |
|
|
D.121
|
`The work of the Fields medallists. Dr. K.F. Roth'. (Bibliog. 121). 5pp. typescript draft with ms. corrections; set of page-proofs. |
1958 |
|
D.122
|
`Cubic forms in 32 variables'. (Bibliog. 116). 74pp. ms. draft. |
1959 |
|
D.123, D.124
|
`Cubic forms in 32 variables'. (Bibliog. 116). 2 copies of 75pp. typescript draft, both with different ms. corrections. |
1959 |
|
D.125
|
`Cubic forms in 32 variables'. (Bibliog. 116). 25pp. ms. draft, paginated 73-97, and headed `8 Synthesis'. |
1959 |
|
D.126
|
`Cubic forms in 32 variables'. (Bibliog. 116). 14pp. ms. draft headed `Cubic Forms. "Absolute" lemmas'. |
1959 |
|
D.127
|
`Cubic forms in 32 variables'. (Bibliog. 116). 1p. ms. notes headed `History of cubic forms in 32 (later 16) variables'; 26pp. ms. draft headed 'B. Certain exponential sums'. (D.127, D.128 are the contents of a folder inscribed `Cubic forms (old) historical interest'.). |
1959 |
|
D.128
|
`Cubic forms in 32 variables'. (Bibliog. 116). 16pp. ms. draft headed `G. Synthesis'. (D.127, D.128 are the contents of a folder inscribed `Cubic forms (old) historical interest'.). |
1959 |
|
D.129
|
`Indefinite quadratic forms', with D. Ridout. (Bibliog. 120). 8pp. ms. and typescript draft and notes, partially paginated, including 1p. in another hand. |
1959 |
|
D.130
|
`Indefinite quadratic forms', with D. Ridout. (Bibliog. 120). 26pp. ms. draft. |
1959 |
|
D.131
|
`Indefinite quadratic forms', with D. Ridout. (Bibliog. 120). Set of page-proofs with ms. corrections. |
1959 |
|
D.132
|
`Some recent progress in analytic number theory'. (Bibliog. 123). 12pp. typescript draft with ms. corrections; copy of J.Lond.Math.Soc., April 1960, including paper. |
1960 |
|
D.133
|
`On a theorem of P.J. Cohen'. (Bibliog. 125). 2 ms. drafts, 7pp. and 8pp. |
1960 |
|
D.134
|
`Über einige neuere Fortschritte der additiven Zahlentheorie'. (Bibliog. 127). 2 ms. drafts, 15pp. and 16pp. |
1960 |
|
D.135
|
`On Weyl's inequality and Waring's problem for cubes', with S. Chowla. (Bibliog. 124). 29pp. ms. draft. |
1961 |
|
D.136
|
`On Weyl's inequality and Waring's problem for cubes', with S. Chowla. (Bibliog. 124). 8pp. ms. draft `re 124' and 5pp. ms. draft. |
1961 |
|
D.137
|
Publications`A note on binary cubic forms'. (Bibliog. 126). 2 ms. drafts, 9pp. and 11pp; correspondence. |
1961 |
|
D.138
|
`Equations of the form f(x) = g(y)', with D.J. Lewis and A. Schinzel. (Bibliog. 129). 13pp. ms. and typescript draft with ms. corrections. |
1961 |
|
D.139
|
`Cubic forms in 29 variables'. (Bibliog. 130). 23pp. typescript draft with ms. corrections. |
1962 |
|
D.140
|
`The addition of norm forms', with B.J. Birch and D.J. Lewis. (Bibliog. 131). 13pp. ms. draft. |
1962 |
|
D.141
|
`The addition of norm forms', with B.J. Birch and D.J. Lewis. (Bibliog. 131). 16pp. ms. draft, with 5pp. ms. notes. |
1962 |
|
D.142
|
`A note on Diophantine approximation'. (Bibliog. 133). 7pp. typescript draft with ms. corrections. |
1962 |
|
D.143
|
`Exponential sums in many variables', with D.J. Lewis. (Bibliog. 135). 34pp. ms. draft with covering note to `Bryan' (Birch). |
1962 |
|
D.144
|
`Cubic forms in sixteen variables'. (Bibliog. 134). Set of galley-proofs with ms. corrections. |
1963 |
|
D.145
|
`Notes on congruences (I)', with D.J. Lewis. (Bibliog. 136). 2 typescript drafts with ms. corrections, 9pp. and 12pp. |
1963 |
|
D.146
|
`Notes on congruences (I)', with D.J. Lewis. (Bibliog. 136). Set of page-proofs with ms. corrections; 2pp. ms. notes. |
1963 |
|
D.147
|
`Notes on congruences (II)', with D.J. Lewis. (Bibliog. 137). 15pp. ms. draft with corrections. |
1963 |
|
D.148
|
`Homogeneous additive equations', with D.J. Lewis. (Bibliog. 138). 46pp. ms. draft with corrections; note to publisher. |
1963 |
|
D.149
|
`A problematic identity'. (Bibliog. 140). 6pp. ms. draft. |
1963 |
|
D.150
|
`A note on Diophantine approximation (II)'. (Bibliog. 144). 15pp. ms. draft with corrections. |
1964 |
|
D.151
|
`Two problems concerning polynomials', with A. Schinzel. (Bibliog. 146). 13pp. ms. draft; 12pp. typescript draft with ms. corrections. |
1964 |
|
D.152
|
`Two problems concerning polynomials', with A. Schinzel. (Bibliog. 146). 5pp. ms. notes by A. Schinzel, dated 9.3.64, possibly work for this paper (or for Bibliog. 145). |
1964 |
|
D.153
|
`Non-homog. cubic eqns', with D.J. Lewis. (Bibliog. 148). 10pp. ms. draft, beginning: `This is an account of a paper by Lewis and myself which has been submitted to PLMS'. |
1964 |
|
D.154
|
`On a theorem of Mrs. Turán'. (Bibliog. 153). 8pp. heavily-corrected ms. draft, and photocopy of original version without corrections. |
1965 |
|
D.155
|
`On a theorem of Mrs. Turán'. (Bibliog. 153). 7pp. photocopy of ms. draft with ms. corrections, and a covering letter to B.J. Birch, 8 July 1964. |
1965 |
|
D.156
|
`y² - x³. 6pp. ms. draft with 2pp. ms. notes, labelled `Early version, eventually published as 159'. |
?1965 |
|
D.157
|
7pp. untitled ms. draft, labelled `m/s of 158 (first folio missing)'. Papers. |
?1966 |
|
D.158
|
`Looking back'. (Bibliog. 162). 16pp. typescript with ms. corrections. |
1966 |
|
D.159
|
`Small differences between prime numbers', with E. Bombieri. (Bibliog. 163). 33pp. photocopy of ms. draft, marked up for print. |
1966 |
|
D.160
|
`A note on certain arithmetical constants', with A. Schinzel. (Bibliog. 165). 7pp. typescript draft with ms. corrections. |
1966 |
|
D.161
|
`Cubic equations of additive type', with D.J. Lewis. (Bibliog. 167). 68pp. typescript draft with ms. corrections. |
1966 |
|
D.162
|
`Notes on congruences III', with D.J. Lewis. (Bibliog. 169). 8pp. typescript draft, with 1p. ms. list of references and 1p. ms. calculations. |
1966 |
|
D.163
|
`Eline Bemerkung Uber Dirichlets L-Funktionen'. (Bibliog. 171). 17pp. ms. draft with corrections. |
1966 |
|
D.164
|
`Diophantine approximation and sums of roots of unity', with A. Schinzel. (Bibliog. 166). Correspondence, chiefly with A. Schinzel, re paper, November 1965-October 1966. |
1967 |
|
D.165
|
`Diophantine approximation and sums of roots of unity', with A. Schinzel. (Bibliog. 166). Miscellaneous ms. notes and drafts. |
1967 |
|
D.166
|
`Diophantine approximation and sums of roots of unity', with A. Schinzel. (Bibliog. 166). `A problem connected with Diophantine approximation'. 6pp. ms. draft. `Diophantine approximation and roots of unity'. 8pp. ms. draft. |
1967 |
|
D.167
|
`Diophantine approximation and sums of roots of unity', with A. Schinzel. (Bibliog. 166). 21pp. ms. draft with corrections, labelled `Version of 166'. |
1967 |
|
D.168
|
`Diophantine approximation and sums of roots of unity', with A. Schinzel. (Bibliog. 166). 15pp. ms. draft with corrections. |
1967 |
|
D.169
|
`Diophantine approximation and sums of roots of unity', with A. Schinzel. (Bibliog. 166). Photocopy of typescript draft, with ms. corrections and additions. |
1967 |
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D.170-D.182
|
`Multiplicative number theory', 1967. |
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D.183
|
`On the large sieve method', with E. Bombieri. (Bibliog. 172). 17pp. ms. draft with corrections. |
1968 |
|
D.184
|
`On the representation of positive integers as sums of three cubes of positive rational numbers', with E. Landau. (Bibliog. 174). This paper was published in a memorial volume to Landau; the work had actually been done in 1935. Ms. notes and calculations, including 2 paginated sequences, 5pp. and 4pp. 6pp. notes by Landau. |
1968 |
|
D.185
|
`On the representation of positive integers as sums of three cubes of positive rational numbers', with E. Landau. (Bibliog. 174). This paper was published in a memorial volume to Landau; the work had actually been done in 1935. 5pp. ms. draft; corrected proofs. Also included is a letter from Marianne Landau on the death of her husband. |
1968 |
|
D.186
|
`Bases for finite fields'. (Bibliog. 175). Extensive ms. drafts and calculations. |
1968 |
|
D.187
|
`Bases for finite fields'. (Bibliog. 175). 38pp. ms. draft with corrections. |
1968 |
|
D.188
|
`A theorem on linear forms', with W.M. Schmidt. (Bibliog. 177). 23pp. photocopy of typescript draft. |
1968 |
|
D.189
|
`A note on Thue's theorem'. (Bibliog. 180). 23pp. ms. draft `Note on the Thue-Siegel Theorem'. |
1968 |
|
D.190
|
`A note on Thue's theorem'. (Bibliog. 180). 3pp. ms. draft on `Siegal's Theorem'. |
1968 |
|
D.191
|
`A note on Thue's theorem'. (Bibliog. 180). 6pp. and 11pp. drafts and calculations on `Thue's Theorem'. |
1968 |
|
D.192
|
`A note on Thue's theorem'. (Bibliog. 180). 26pp. ms. draft. |
1968 |
|
D.193
|
`A note on Thue's theorem'. (Bibliog. 180). Corrected version of D.192 (photocopy). |
1968 |
|
D.194
|
`Some inequalities involving trigonometrical polynomials', with E. Bombieri. (Bibliog. 181). 23pp. ms. draft. |
1969 |
|
D.195
|
`Some inequalities involving trigonometrical polynomials', with E. Bombieri. (Bibliog. 181). 14pp. photocopy of `note on the large sieve inequality', with E. Bombieri. Early version of Bibliog. 181. |
1969 |
|
D.196
|
`Correspondence with Baker relevant to 182, and two m/s'. Contents of a folder so inscribed. Three letters from Davenport to A. Baker, July, September 1967, re material for joint paper published in 1969 (Bibliog. 182). (Information from Professor B.J. Birch, February 1986.). |
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D.197
|
`Correspondence with Baker relevant to 182, and two m/s'. Contents of a folder so inscribed. `The numerical determination of rational approximations'. 6pp. draft. `A non-homogeneous linear form in 2 variables'. 4pp. ms. draft. |
|
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D.198
|
`Approx. to a real number by alg-integers', with W.M. Schmidt. (Bibliog. 183). 6pp. ms. draft. |
1969 |
|
D.199
|
`Simultaneous equations of additive type', with D.J. Lewis. (Bibliog. 184). 105pp. photocopy of ms. draft with corrections; 4pp. ms. summary. |
1969 |
|
D.200
|
Publications. Biographical article on G.H. Hardy commissioned by `The Encyclopedia Americana'. Correspondence, January, February 1969; 2pp. ms. draft. |
1969 |
|
D.201
|
`On writing mathematical papers'. (Unpublished). Correspondence, 1966, 1969; 2pp. ms. notes. |
1969 |
|
D.202
|
`On writing mathematical papers'. (Unpublished). Background material (printed matter). |
1969 |
|
D.203
|
`On writing mathematical papers'. (Unpublished). 23pp. typescript draft with covering letter to Mrs. Davenport from L.J. Mordell, June 1969. Letters to Mrs. Davenport re paper from J.W.S. Cassels, October 1969, and V. Armitage, February 1970. |
1969 |
|
D.204
|
`Two additive equations', with D.J. Lewis. (Bibliog. 186). 32pp. photocopy of typescript draft with ms. corrections. |
1971 |
|
D.205
|
`Homogeneous quadratic equations'. (Bibliog. 194). 10pp. photocopy of typescript draft. |
1971 |
|
D.206
|
`Gaps between values of positive definite quadratic forms', with D.J. Lewis. (Bibliog. 195). 27pp. photocopy of typescript draft; 1p. instructions to printer; 1p. corrections. |
1971 |
|
D.207
|
Publications. `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 correspondence on the large sieve inequality; specifically, Halberstam had asked Davenport whether the inequality might not have some applications in the theory of trigonometrical polynomials and the note came in reply to this query.'. 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. |
1972 |
|
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. |
1938–1964 |
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D.209
|
Publications. 3pp. incomplete typescript draft of letter concerning a book, not by Davenport. |
nd |
|
D.210-D.213
|
`The collected works of Harold Davenport', edited by B.J. Birch, H. Halberstam and C.A. Rogers, 1977. |
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