Identities on poly-Dedekind sums
Number Theory
2020-09-11 v1
Abstract
Dedekind sums occur in the transformation behaviour of the logarithm of the Dedekind eta-function under substitutions from the modular group. In 1892, Dedekind showed a reciprocity relation for the Dedekind sums. Apostol generalized Dedekind sums by replacing the first Bernoulli function appearing in them by any Bernoulli functions and derived a reciprocity relation for the generalized Dedekind sums. In this paper, we consider poly-Dedekind sums which are obtained from the Dedekind sums by replacing the first Bernoulli function by any type 2 poly-Bernoulli functions of arbitrary indices and prove a reciprocity relation for the poly-Dedekind sums.
Keywords
Cite
@article{arxiv.2009.04853,
title = {Identities on poly-Dedekind sums},
author = {Taekyun Kim and Dae san Kim and Hyunseok Lee and Lee-Chae Jang},
journal= {arXiv preprint arXiv:2009.04853},
year = {2020}
}
Comments
12 pages