2020/09/10 by Taekyun Kim, Kim, Taekyun, Dae San Kim +6
Mathematics · #11B68 #11B8 #11F20 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #math.NT #msc:11B68 #msc:11B8 #msc:11F20
paper · pdf · doi:10.48550/arxiv.2009.04853
12 pages
arxiv created 2020/09/10 · openalex publication_date 2020/09/10 · arxiv updated 2020/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.