Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-21T13:20:16.715Z Has data issue: false hasContentIssue false
  • English
  • Français

On exponential sums over prime numbers

Part of: Exponential sums and character sums

Published online by Cambridge University Press:  09 April 2009

A. Sárközy  and
C. L. Stewart
A. Sárközy
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, Reáltanoda u. 13–16 Budapest, H-1053, Hungary
C. L. Stewart
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this article we establish an estimate for a sum over primes that is the analogue of an estimate for a sum over consecutive integers which has proved to be very useful in applications of exponential sums to problems in number theory.

MSC classification

Secondary: 11L40: Estimates on character sums
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 3 , June 1989 , pp. 423 - 437
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Montgomery, H. L. and Vaughan, R. C., ‘The large sieve’, Mathematika 20 (1973), 119–134.CrossRefGoogle Scholar
[2]Prachar, K., Primzahlverteilung (Springer-Verlag, 1957).Google Scholar
[3]Sárközy, A. and Stewart, C. L., ‘On divisors of sums of integers, II’, J. Reine Angew. Math. 365 (1986), 171–191.Google Scholar
[4]Vaughan, R. C., ‘On the distribution of ap modulo 1’, Mathematika 24 (1977), 135–141.CrossRefGoogle Scholar
[5]Vinogradov, I. M., The method of trigonometric sums in the theory of numbers (Interscience, New York, 1954).Google Scholar