PreprintCC BY 4.0arXiv
Reciprocity formulas for generalized Dedekind character sums
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.
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BibTeX
@misc{he2026reciprocity,
title = {{Reciprocity formulas for generalized Dedekind character sums}},
author = {Yuan He},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39075},
eprint = {2610.39075},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39075},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reciprocity formulas for generalized Dedekind character sums
AU - Yuan He
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39075
UR - https://arxiv.org/abs/2610.39075
AB - 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.
ER -