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Research Article | Open Access

A new reciprocity formula of Dedekind sums and its applications

Zhuoyu Chen1, Wenpeng Zhang2( )
School of Freshmen, Xi'an Technological University, Xi'an 710021, China
School of Science, Xi'an Technological University, Xi'an 710021, China
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Abstract

Our main purpose of this article was using the analytic methods and the properties of Dirichlet L-functions to study the properties of Dedekind sums and give a new reciprocity formula for it. As its applications, some exact calculating formula for one kind mean square value of Dirichlet L-fuctions with the weight of the character sums were obtained.

Keywords

Dedekind sumsreciprocity formulaDirichlet L-functionsthe mean square value of L-function
CLC number: 11F20, 11M20

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AIMS Mathematics
Volume 9 Issue 5,
May 2024
Pages 12814-12824
DOI: 10.3934/math.2024626

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Cite this article:
Chen Z, Zhang W. A new reciprocity formula of Dedekind sums and its applications. AIMS Mathematics, 2024, 9(5): 12814-12824. https://doi.org/10.3934/math.2024626

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Received: 27 February 2024
Revised: 21 March 2024
Accepted: 26 March 2024
Published: 15 May 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)