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Research Article | Open Access

A note on the hybrid power mean involving the cubic Gauss sums and Kloosterman sums

Xiaoxue Li1( ), Wenpeng Zhang2
School of Science, Xi'an Aeronautical Institute, Xi'an, Shaanxi, China
School of Mathematics, Northwest University, Xi'an, Shaanxi, China
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Abstract

The main purpose of this paper is to study the calculating problem of one kind hybrid power mean involving the cubic Gauss sums and Kloosterman sums, and using the elementary methods, analytic methods and the properties of the classical Gauss sums to give some interesting calculating formula for them. At the same time, the paper also provides an effective calculating method for the study of the hybrid power mean involving the k-th Gauss sums and Kloosterman sums.

Keywords

the cubic Gauss sumsKloosterman sumshybrid power meanelementary methodrecurrence formula
CLC number: 11L03, 11L05

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 16102-16111
DOI: 10.3934/math.2022881

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Cite this article:
Li X, Zhang W. A note on the hybrid power mean involving the cubic Gauss sums and Kloosterman sums. AIMS Mathematics, 2022, 7(9): 16102-16111. https://doi.org/10.3934/math.2022881

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Received: 17 March 2022
Revised: 19 June 2022
Accepted: 22 June 2022
Published: 15 September 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)