Reciprocity formulas for generalized Dedekind character sums

In this paper, we apply the Fourier series technique to establish a new formula for the product of the generalized Bernoulli function and the Bernoulli function. As applications, we derive some reciprocity formulas for generalized Dedekind character sums. In particular, we show that the reciprocity formulas of Berndt, Can, and others follow as special cases.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.39075
Primary Topic
Advanced Mathematical Identities
Type
preprint
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preprint

Reciprocity formulas for generalized Dedekind character sums

Yuan He
arXiv (Cornell University)
Advanced Mathematical Identities
preprint

Reciprocity formulas for generalized Dedekind character sums

Yuan He
preprint en

Abstract

In this paper, we apply the Fourier series technique to establish a new formula for the product of the generalized Bernoulli function and the Bernoulli function. As applications, we derive some reciprocity formulas for generalized Dedekind character sums. In particular, we show that the reciprocity formulas of Berndt, Can, and others follow as special cases.

arXiv (Cornell University)
Advanced Mathematical Identities
DOIOpen Access PDFOpenAlex
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Reciprocity formulas for generalized Dedekind character sums — Yuan He · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS