An asymptotic approximation for incomplete Gauss sums

Authors:
R. B. Paris
Affiliations:
Division of Mathematical Sciences, University of Abertay Dundee, Dundee DD1 1HG, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

Citing 2
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An asymptotic approximation for incomplete Gauss sums. II

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Abstract

The classical incomplete Gauss sum@?j=0m-1exp(2@pij^p/N)(1=1)is studied for large N. An expansion is derived for this sum when p is an integer that holds uniformly for 1=1. Numerical results are given to demonstrate the accuracy of the various approximations.