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Bombieri's mean value theorem

Published online by Cambridge University Press:  26 February 2010

P. X. Gallagher
P. X. Gallagher
Affiliation:
Barnard College, Columbia University, New York, 27, New York (USA)
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Extract

The purpose of this paper is to give a short proof of an important recent theorem of Bombieri [2] on the mean value of the remainder term in the prime number theorem for arithmetic progressions. Applications of the theorem have been made by Bombieri and Davenport [3], Rodriques [9], and Elliott and Halberstam [5]. For earlier versions of the theorem and a survey of other applications, see Barban [1], and Halberstam and Roth [7, Chapter 4].

Type
Research Article
Information
Mathematika , Volume 15 , Issue 1 , June 1968 , pp. 1 - 6
Copyright
Copyright © University College London 1968

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References

1.Barban, M. B., “The ‘large sieve’ method and its applications in the theory of numbers”, Russian Math. Surveys, 21 (1966), 49–103.CrossRefGoogle Scholar
2.Bombieri, E., “On the large sieve”, Mathematika, 12 (1965), 201–225.CrossRefGoogle Scholar
3.Bombieri, E. and Davenport, H., “Small differences between prime numbers”, Proc. Royal Soc. A., 293 (1966), 1–18.Google Scholar
4.Davenport, H. and Halberstam, H., “The values of a trigonometric polynomial at well spaced points”, Mathematika, 13 (1966), 91–96; 14 (1967), 229.CrossRefGoogle Scholar
5.Elliott, P. D. T. A. and Halberstam, H., “Some applications of Bombieri 's theorem”, Mathematika, 13 (1966), 196–203.CrossRefGoogle Scholar
6.Gallagher, P. X., “The large sieve”, Mathematika, 14 (1967), 14–20.CrossRefGoogle Scholar
7.Halberstam, H. and Roth, K. F., Sequences Vol. 1, (Oxford, 1966).Google Scholar
8.Prachar, K., Primzahlverteilung (Springer, 1957).Google Scholar
9.Rodriques, G., “Sul problema dei divisori di Titchmarsh”, Bollettino Unione Math. Italiana (3), 20 (1965), 358–366.Google Scholar