Identities on poly-Dedekind sums

Dae San Kim; Hyunseok Lee; Lee-Chae Jang; Taekyun Kim

REVIEW

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

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

Identities on poly-Dedekind sums

Taekyun Kim , Dae san Kim , Hyunseok Lee , Lee-Chae Jang This is my paper

classification math.NT

keywords sumsdedekindbernoullipoly-dedekindreciprocityrelationfirstfunction

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

0 comments

read the original 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.

Identities on poly-Dedekind sums

discussion (0)