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Identities on poly-Dedekind sums

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arxiv 2009.04853 v1 pith:H6Q4IOEY submitted 2020-09-10 math.NT

Taekyun Kim , Dae san Kim , Hyunseok Lee , Lee-Chae Jang This is my paper · ORCID
classification math.NT
keywords sumsdedekindbernoullipoly-dedekindreciprocityrelationfirstfunction
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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.

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