Identities on poly-Dedekind sums

Advances in Difference Equations

Taekyun Kim¹  Hyunseok Lee¹  Dae San Kim²  Lee-Chae Jang³ 

[1] Department of Mathematics, Kwangwoon University, 139-701, Seoul, Republic of Korea;Department of Mathematics, Sogang University, 121-742, Seoul, Republic of Korea;Graduate School of Education, Konkuk University, Seoul, Republic of Korea;

关键词: Poly-Dedekind sum;    Polyexponential function;    Type 2 poly-Bernoulli polynomial;    11F20;    11B68;    11B83;   

DOI  :  10.1186/s13662-020-03024-x

来源: Springer

【 摘 要 】

Dedekind sums occur in the transformation behavior 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 the poly-Dedekind sums 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.

【 授权许可】

CC BY