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Research Article | Open Access

On the k-th power mean of one kind generalized cubic Gauss sums

Xiaoge Liu, Yuanyuan Meng( )
Research Center for Number Theory and Its Applications, Northwest University, Xi'an, 710127, Shaanxi, China
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Abstract

The main purpose of this paper is using the elementary methods and properties of the recurrence sequence to study the calculating problem of the k-th power mean of one kind generalized cubic Gauss sums, and give an exact calculating formula for it.

Keywords

the generalized Gauss sumsk-th power meanelementary methodrecurrence sequencecalculating formula
CLC number: 11L03, 11L05

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AIMS Mathematics
Volume 8 Issue 9,
September 2023
Pages 21463-21471
DOI: 10.3934/math.20231093

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Liu X, Meng Y. On the k-th power mean of one kind generalized cubic Gauss sums. AIMS Mathematics, 2023, 8(9): 21463-21471. https://doi.org/10.3934/math.20231093

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Received: 21 February 2023
Revised: 26 June 2023
Accepted: 28 June 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 (https://creativecommons.org/licenses/by/4.0)