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Research Article | Open Access

On the sixth power mean values of a generalized two-term exponential sums

Shujie Zhou1, Li Chen2( )
School of Mathematics and Information Science, Shaanxi Normal University, Xi'an, China
School of Mathematics, Xi'an University of Finance and Economics, Xi'an, China
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Abstract

This paper examines the evaluations of sixth power mean values of a generalized two-term exponential sums. In the case p ≡ 3 mod 4, we try to establish two precise formulas by applying the properties of character sums and the number of the solutions of relevant congruence equations modulo an odd prime p.

Keywords

the two-term exponential sumssixth power mean valueselementary methodcongruence equationcalculating formula
CLC number: 11L03, 11L05

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AIMS Mathematics
Volume 8 Issue 11,
November 2023
Pages 28105-28119
DOI: 10.3934/math.20231438

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Cite this article:
Zhou S, Chen L. On the sixth power mean values of a generalized two-term exponential sums. AIMS Mathematics, 2023, 8(11): 28105-28119. https://doi.org/10.3934/math.20231438

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Received: 15 August 2023
Revised: 02 September 2023
Accepted: 12 September 2023
Published: 15 November 2023
©2023 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)