Some reciprocity formulas for generalized Dedekind-Rademacher sums
Number Theory
2024-03-08 v2
Abstract
In this paper, we study the generalized Dedekind-Rademacher sums considered by Hall, Wilson and Zagier. We establish a formula for the products of two Bernoulli functions. The proof relies on Parseval's formula, Hurwitz's formula, and Lerch's functional equation. The result leads to reciprocity formulas for some generalizations of the classical Dedekind sums. In particular, it is shown that Carlitz's, Berndt's, Hall and Wilson's reciprocity theorems are deduced as special cases.
Keywords
Cite
@article{arxiv.2310.17093,
title = {Some reciprocity formulas for generalized Dedekind-Rademacher sums},
author = {Yuan He and Yong-Guo Shi},
journal= {arXiv preprint arXiv:2310.17093},
year = {2024}
}