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Research Article | Open Access

Generalized polynomial exponential sums and their fourth power mean

Li Wang, Yuanyuan Meng( )
Research Center for Number Theory and Its Applications, Northwest University, Xi'an, China
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Abstract

The study of the power mean of the generalized polynomial exponential sums plays a very important role in analytic number theory, and many classical number theory problems are closely related to it. In this article, we use the elementary methods and the properties of the exponential sums to study the calculating problem of one kind of fourth power mean of some special generalized polynomial exponential sums, and we give some exact calculating formulae for them.

Keywords

generalized polynomial exponential sumsfourth power meanelementary methodexact calculating formula

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Electronic Research Archive
Volume 31 Issue 7,
July 2023
Pages 4313-4323
DOI: 10.3934/era.2023220

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Cite this article:
Wang L, Meng Y. Generalized polynomial exponential sums and their fourth power mean. Electronic Research Archive, 2023, 31(7): 4313-4323. https://doi.org/10.3934/era.2023220

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Received: 22 December 2022
Revised: 15 May 2023
Accepted: 25 May 2023
Published: 15 July 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)