The asymptotics of a new exponential sum

Richard B. Paris

doi:10.1016/j.cam.2008.01.014

The asymptotics of a new exponential sum

Richard B. Paris

Research output: Contribution to journal › Article › peer-review

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Abstract

The absolutely convergent exponential sum [formula missing] is studied for m→+∞ and fixed p when the parameter θ is allowed to become large such that θ/m remains finite. This situation corresponds, in general, to the trace in the complex plane of the partial sums of Sp(θ;m) consisting of a multiple spiral structure. Numerical results are presented to illustrate the accuracy of the expansion.

Original language	English
Pages (from-to)	314-325
Number of pages	12
Journal	Journal of Computational and Applied Mathematics
Volume	223
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2008.01.014
Publication status	Published - 1 Jan 2009

Keywords

Exponential sums
Gauss sum
Asymptotics
Curlicues

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10.1016/j.cam.2008.01.014

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AB - The absolutely convergent exponential sum [formula missing] is studied for m→+∞ and fixed p when the parameter θ is allowed to become large such that θ/m remains finite. This situation corresponds, in general, to the trace in the complex plane of the partial sums of Sp(θ;m) consisting of a multiple spiral structure. Numerical results are presented to illustrate the accuracy of the expansion.

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The asymptotics of a new exponential sum

Abstract

Keywords

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