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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
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
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- Research Article
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- Copyright © University College London 1992
References
1.Bombieri, E.. On twin almost primes. Acta Aritk., 28 (1975), 177–193; Corrigendum,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
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