A new reciprocity formula of Dedekind sums and its applications

Zhuoyu Chen; Wenpeng Zhang; Zhuoyu Chen; Wenpeng Zhang

doi:10.3934/math.2024626

AIMS Mathematics

2024, Volume 9, Issue 5: 12814-12824. doi: 10.3934/math.2024626

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A new reciprocity formula of Dedekind sums and its applications

Zhuoyu Chen ¹,
Wenpeng Zhang ^{2
,
,}

1.
School of Freshmen, Xi'an Technological University, Xi'an 710021, China
2.
School of Science, Xi'an Technological University, Xi'an 710021, China
^†Dedicated to Professor Taekyun Kim on the occasion of his sixtieth birthday

Received: 27 February 2024 Revised: 21 March 2024 Accepted: 26 March 2024 Published: 03 April 2024
MSC : 11F20, 11M20

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.
- Dedekind sums,
- reciprocity formula,
- Dirichlet $ L $-functions,
- the mean square value of $ L $-function
Citation: Zhuoyu Chen, Wenpeng Zhang. A new reciprocity formula of Dedekind sums and its applications[J]. AIMS Mathematics, 2024, 9(5): 12814-12824. doi: 10.3934/math.2024626

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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.

References

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