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Research Article | Open Access

Fourth power mean values of one kind special Kloosterman's sum

Li Rui1, Nilanjan Bag2( )
Department of Mathematics, Longnan Teachers College, Longnan, Gansu, China
Department of Mathematics, Ramakrishna Mission Vivekananda Educational and Research Institute, Belur Math, Howrah, India
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Abstract

The main purpose of this article is using the analytic methods and properties of classical Gauss sums to study the calculating problem of fourth power mean values of one kind special Kloosterman's sum, and give a sharp asymptotic formula for it. At the same time, the paper also provides a new and effective method for the study of related power mean value problems.

Keywords

special Kloosterman's sumsfourth power meananalytic methodasymptotic formula
CLC number: 11L03; 11L05

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Electronic Research Archive
Volume 31 Issue 10,
October 2023
Pages 6445-6453
DOI: 10.3934/era.2023326

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Cite this article:
Rui L, Bag N. Fourth power mean values of one kind special Kloosterman's sum. Electronic Research Archive, 2023, 31(10): 6445-6453. https://doi.org/10.3934/era.2023326

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Received: 15 June 2023
Revised: 03 September 2023
Accepted: 15 September 2023
Published: 15 October 2023
©2023 the Author(s), licensee AIMS Press.

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