Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T21:22:06.379Z Has data issue: false hasContentIssue false
  • English
  • Français

The distribution of exponential sums

Published online by Cambridge University Press:  26 February 2010

J. H. Loxton
J. H. Loxton
Affiliation:
School of Mathematics, University of New South Wales, Kensington, N.S.W., Australia, 2033.
Get access

Extract

We shall consider incomplete exponential sums of the shape

where q, a and h are integers satisfying 1 ≤ a < a + h ≤ q, f(x) is a function denned at least for the integers in the range of summation, and eq(t) is an abbreviation for e2πit/q.

Type
Research Article
Information
Mathematika , Volume 32 , Issue 1 , June 1985 , pp. 16 - 25
Copyright
Copyright © University College London 1985

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.Feller, W.. An introduction to probability theory and its applications, Volume 2 (Wiley, 1966).Google Scholar
2.Hooley, C.. On the greatest prime factor of a cubic polynomial. J. reine angew. Math., 303/304 (1978), 21–50.CrossRefGoogle Scholar
3.Lehmer, D. H.. Incomplete Gauss sums. Mathematika, 23 (1976), 125–135.CrossRefGoogle Scholar
4.Loxton, J. H.. The graphs of exponential sums. Mathematika, 30 (1983), 153–163.CrossRefGoogle Scholar
5.Watson, G. N.. A treatise on the theory of Besselfunctions (Cambridge University Press, 1948).Google Scholar