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Small differences between consecutive primes II

Published online by Cambridge University Press:  26 February 2010

M. N. Huxley
M. N. Huxley
Affiliation:
University College, Cardiff
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Extract

§1. Let pi denote the i-th prime number, and let

The prime number theorem implies Er ≤ r. Bombieri and Davenport [1] showed that

improving earlier results of Erdős, Rankin and Ricci. Their basic result (corresponding to Lemma 1 below) counts pairs of primes differing by 2n with some weight t(n).

Type
Research Article
Information
Mathematika , Volume 24 , Issue 2 , December 1977 , pp. 142 - 152
Copyright
Copyright © University College London 1977

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References

1.Bombieri, E. and Davenport, H.. “Small differences between prims numbers”, Proc. Roy. Soc. A, 293 (1966) 1–18.Google Scholar
2.Huxley, M. N.. “On the differences of primes in arithmetic progressions”, Acta Arithmetica, 15 (1969), 367–392.CrossRefGoogle Scholar
3.Huxley, M. N.. “Small differences between consecutive primes”, Mathematika, 20 (1973), 229–232.CrossRefGoogle Scholar
4.Pilt'ai, G. Z.. “On the size of the difference between consecutive primes”, Issledovania po teorii chisel, 4 (1972), 73–79.Google Scholar