Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-23T12:55:11.517Z Has data issue: false hasContentIssue false
  • English
  • Français

The graphs 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, New South Wales, Australia, 2033.
Get access

Extract

In [3], D. H. Lehmer has analysed the incomplete Gaussian sum

where N and q are positive integers with N < q and e(x) is an abbreviation for e2πix. The crucial observation is that, for almost all values of N, Gq(N) is in the vicinity of the point ¼(1 + i)q1/2. This leads to sharp estimates of the shape Gq(N) = O(q½).

Type
Research Article
Information
Mathematika , Volume 30 , Issue 2 , December 1983 , pp. 153 - 163
Copyright
Copyright © University College London 1983

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.Jahnke, E. and Emde, F.. Tables of Junctions with formulae and curves (Dover, 1943).Google Scholar
2.Landau, E.. Vorlesungen über Zahlentheorie, Volume 2 (Dover, 1947).Google Scholar
3.Lehmer, D. H.. Incomplete Gauss sums. Mathematika, 23 (1976), 125–135.CrossRefGoogle Scholar
4.Loxlon, J. H.. Captain Cook and the Loch Ness monster. James Cook Mathematical Notes, 3 (1981), 3060–3064.Google Scholar
5.Rademacher, H.. Topics in analytic number theory (Springer, 1973).CrossRefGoogle Scholar