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Research Article | Open Access

A remark for Gauss sums of order 3 and some applications for cubic congruence equations

Wenxu Ge1, Weiping Li2( ), Tianze Wang1
School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China
School of Mathematics and Information Sciences, Henan University of Economics and Law, Zhengzhou 450046, China
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Abstract

In this paper, we give some relations between Gauss sums of order 3. As application, we give the number of solutions of some cubic diagonal equations. These generalize the earlier results obtained by Hong-Zhu and solve the sign problem raised by Zhang-Zhang.

Keywords

Gauss sumexponential sumdiagonal cubic formcongruence equationsprime
CLC number: 11T23, 11T24

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AIMS Mathematics
Volume 7 Issue 6,
June 2022
Pages 10671-10680
DOI: 10.3934/math.2022595

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Cite this article:
Ge W, Li W, Wang T. A remark for Gauss sums of order 3 and some applications for cubic congruence equations. AIMS Mathematics, 2022, 7(6): 10671-10680. https://doi.org/10.3934/math.2022595

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Received: 03 October 2021
Revised: 17 March 2022
Accepted: 21 March 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

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