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On Bombieri and Davenport's theorem concerning small gaps between primes

Part of: Multiplicative number theory

Published online by Cambridge University Press:  26 February 2010

D. A. Goldston
D. A. Goldston
Affiliation:
Department of Mathematics and Computer Science, San Jose State University, San Jose, CA 95192, USA.
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Extract

§1. Introduction. In this paper we give a new proof of a theorem of Bombieri and Davenport [2, Theorem 1]. Let t(–k) = t(k) be real,

where e(u) = e2πiu. Let p and p' denote primes, k an integer, and define

MSC classification

Secondary: 11N05: Distribution of primes
Type
Research Article
Information
Mathematika , Volume 39 , Issue 1 , June 1992 , pp. 10 - 17
Copyright
Copyright © University College London 1992

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References

1.Bombieri, E.. On twin almost primes. Acta Aritk., 28 (1975), 177–193; Corrigendum,CrossRefGoogle Scholar
Bombieri, E.. On twin almost primes. Acta Aritk., 28 (1976), 457–461.CrossRefGoogle Scholar
2.Bombieri, E. and Davenport, H.. Small differences between prime numbers. Proc. Roy. Soc. A, 293 (1966), 1–18.Google Scholar
3.Bombieri, E., Friedlander, J. B. and Iwaniec, H.. Primes in arithmetic progressions to large moduli. III. J. of the American Math. Soc., 2 (1989), 215–224.CrossRefGoogle Scholar
4.Goldston, D. A.. Linnik's theorem on Goldbach numbers in short intervals. Glasgow Math. J., 32 (1990), 285–297.CrossRefGoogle Scholar
5.Goldston, D. A.. On Hardy and Littlewood's Contribution to the Goldbach Conjecture. Submitted, 1989 Amalfi Conference proceedings.Google Scholar
6.Graham, S.. An asymptotic estimate related to Selberg's sieve. J. of Number Theory, 10 (1978), 83–94.CrossRefGoogle Scholar
7.Hardy, G. H. and Wright, E. M.. An Introduction to the Theory of Numbers, 4th ed. (Oxford Univ. Press, Oxford, 1960).Google Scholar
8.Heath-Brown, D. R.. The ternary Goldbach problem. Revista Matemática Iberoamericana, 1 (1985), 45–59.CrossRefGoogle Scholar
9.Huxley, M. N.. Irregularity in shifted sequences. J. of Number Theory, 4 (1972), 437–454.CrossRefGoogle Scholar
10.Huxley, M. N.. Small differences between prime numbers II. Mathematika, 24 (1977), 142–152.CrossRefGoogle Scholar
11.Maier, Helmut. Small differences between prime numbers. Michigan Math. J., 35 (1988), 323–344.CrossRefGoogle Scholar
12.Turán, P.. On the twin prime problem I. Publ. Math. Inst. Hung. Acad. Sci. Ser. 4. 9 (1964), 247–261.Google Scholar