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Papers of Harold Davenport Halberstam, Heini (1926-2014) mathematician
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'Trigonometrical polynomials'

'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.

'The collected works of Harold Davenport', edited by B. J. Birch, H. Halberstam and C. A. Rogers

210: Correspondence between the editors and with other colleagues, 1969, 1970
211: Correspondence between the editors and with other colleagues, 1974
212: Correspondence between the editors and with other colleagues, 1975
213: B. J. Birch's ms. notes for and drafts of introductions to papers by Davenport. Photocopies of Davenport's typescript notes on his own work. Part only; for full version see A.10. 4pp. typescript index, with ms. corrections by B. J. Birch.

Bombieri, E. and others

G.28: 1963–64. Includes Davenport's report on Bombieri's work in Cambridge 1963-64 and arrangements for Davenport to lecture in Milan.
G.29: Jan.-July 1965. Correspondence, notes and calculations; includes draft paper by Bombieri on 'The Statistical theory of Dirichlet L-functions'.
G.30: Aug. 1965. Correspondence and drafts on primes paper (published Proc.Roy.Soc. A, 1966).
G.31: Aug. 1965. 'Small differences of primes', two ms. drafts, one each by Davenport and Bombieri, related to correspondence.
G.32: Sept.-Dec. 1965. Continuing correspondence and drafts, on 'prime numbers' paper and on 'large sieve' paper (published 1968).
G.33: Jan.-Apr. 1966.
G.34: June-Sept. 1966. Includes letter from H. Halberstam.
G.35: Oct.-Dec. 1966. Mainly on sieve paper.
G.36: Extensive notes by Davenport kept with 1966 correspondence.
G.37: 1967. Includes revised version of 'large sieve method' July, and correspondence on polynomials (leading up to collaborative paper published in 1969.)
G.38: Jan.-July 1968. Includes arrangements re publication of 'large sieve' paper, and a 7 pp. ms. by Davenport 'The case small', and letters of comment.
G.39: 1969. Also includes press-cutting re award to Bombieri of the Fields medal at International Mathematical Congress, Vancouver, 1974.

Correspondence and material relating to the memoir of Davenport by C. A. Rogers, D. A. Burgess, H. Halberstam and B. J. Birch

Correspondence and material relating to the memoir of Davenport by C.A. Rogers, D.A. Burgess, H. Halberstam and B.J. Birch (Biographical Memoirs of Fellows of the Royal Society, 17, 1971).

Includes 2pp. plan allocating work between collaborators, correspondence, drafts of various sections of the memoir.