Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-16T17:09:37.121Z Has data issue: false hasContentIssue false
  • English
  • Français

On the large sieve

Published online by Cambridge University Press:  26 February 2010

E. Bombieri
E. Bombieri
Affiliation:
Istituto Matematico, Via C. Saldini 50, Milan.
Get access

Extract

The purpose of this paper is to give a new and improved version of Linnik's large sieve, with some applications. The large sieve has its roots in the Hardy-Littlewood method, and in its most general form it may be considered as an inequality which relates a singular series arising from an integral where S(α) is any exponential sum, to the integral itself.

Type
Research Article
Information
Mathematika , Volume 12 , Issue 2 , December 1965 , pp. 201 - 225
Copyright
Copyright © University College London 1965

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Roth, K. F. “On the large sieve of Linnik and Rényi”, Mathematika, 12 (1965), 1–9.CrossRefGoogle Scholar
2.Linnik, Yu. V., “The large sieve”, Doklady Akad. Nauk SSSR, 30 (1941), 292–294 (in Russian).Google Scholar
3.Rényi, A., “On the representation of an even number as the sum of a single prime and an almost prime number”, Izv. Akad. Nauk SSSR, Ser. Mat. 12 (1948), 57–78 (in Russian); also American Math. Soc. Translations (2), 19 (1961), 299–321.Google Scholar
4.Prachar, K., Primzahlverteilung (Springer, 1957).Google Scholar
5.Titchmarsh, E. C., The theory of the Riemann zeta-function (Oxford, 1951).Google Scholar
6.Gabriel, R. M., “Some results concerning the integrals of moduli of regular functions along certain curves”, Journal London Math. Soc., 2 (1927), 112–117.CrossRefGoogle Scholar