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Research Article | Open Access

The fourth power mean of the generalized quadratic Gauss sums associated with some Dirichlet characters

Xuan Wang1, Li Wang1, Guohui Chen2( )
Research Center for Number Theory and Its Applications, Northwest University, Xi'an 710127, China
College of Mathematics and Statistics, Hainan Normal University, Hainan 571100, China
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Abstract

In this paper, the fourth power mean values of the generalized quadratic Gauss sums associated with the 3-order and 4-order Dirichlet characters are given by using the properties of the Dirichlet characters and Gauss sums.

Keywords

generalized quadratic Gauss sumsthe fourth power meank-order Dirichlet charactercalculating formula
CLC number: 11L03, 11L05

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AIMS Mathematics
Volume 9 Issue 7,
July 2024
Pages 17774-17783
DOI: 10.3934/math.2024864

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Cite this article:
Wang X, Wang L, Chen G. The fourth power mean of the generalized quadratic Gauss sums associated with some Dirichlet characters. AIMS Mathematics, 2024, 9(7): 17774-17783. https://doi.org/10.3934/math.2024864

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Received: 15 March 2024
Revised: 02 May 2024
Accepted: 14 May 2024
Published: 15 July 2024
©2024 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)