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Research Article | Open Access

On two-term exponential sums and their mean values

Jianghua Li( ), Zepeng Zhang, Tianyu Pan
College of Sciences, Xi'an University of Technology, Xi'an, Shaanxi, China
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Abstract

The mean value problems of exponential sums play a very important role in the research of analytic number theory, and many famous number theory problems are closely related to them. The main purpose of this paper is using some elementary methods and the number of the solutions of the congruence equations to study the calculating problem of some fourth power means of two-term exponential sums, and give exact calculating formulae and asymptotic formula for them.

Keywords

the two-term exponential sumsfourth power meanelementary methodcalculating formula

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Electronic Research Archive
Volume 31 Issue 9,
September 2023
Pages 5559-5572
DOI: 10.3934/era.2023282

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Cite this article:
Li J, Zhang Z, Pan T. On two-term exponential sums and their mean values. Electronic Research Archive, 2023, 31(9): 5559-5572. https://doi.org/10.3934/era.2023282

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Received: 23 January 2023
Revised: 21 April 2023
Accepted: 25 July 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)