An asymptotic approximation for incomplete Gauss sums

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摘要

The classical incomplete Gauss sum∑j=0m-1exp(2πijp/N)(1⩽m1)is studied for large N. An expansion is derived for this sum when p is an integer that holds uniformly for 1⩽m1. Numerical results are given to demonstrate the accuracy of the various approximations.

论文关键词:Incomplete Gauss sum,Exponential sums,Asymptotics,Curlicues

论文评审过程:Received 21 May 2004, Revised 4 September 2004, Available online 28 December 2004.

论文官网地址:https://doi.org/10.1016/j.cam.2004.11.013