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

1 Citation (Scopus)

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

Access to Document

10.1016/j.cam.2008.01.014

Cite this

@article{793f220784064f64a9b33f070130605b,

title = "The asymptotics of a new exponential sum",

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.",

author = "Paris, \{Richard B.\}",

year = "2009",

month = jan,

day = "1",

doi = "10.1016/j.cam.2008.01.014",

language = "English",

volume = "223",

pages = "314--325",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier B.V.",

number = "1",

}

TY - JOUR

T1 - The asymptotics of a new exponential sum

AU - Paris, Richard B.

PY - 2009/1/1

Y1 - 2009/1/1

N2 - 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.

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.

U2 - 10.1016/j.cam.2008.01.014

DO - 10.1016/j.cam.2008.01.014

M3 - Article

SN - 0377-0427

VL - 223

SP - 314

EP - 325

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

The asymptotics of a new exponential sum

Abstract

Keywords

Access to Document

Fingerprint

Cite this