Identities on poly-Dedekind sums

Abstract 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 app...

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Main Authors:	Taekyun Kim, Dae San Kim, Hyunseok Lee, Lee-Chae Jang
Format:	Article
Language:	English
Published:	SpringerOpen 2020-10-01
Series:	Advances in Difference Equations
Subjects:	Poly-Dedekind sum Polyexponential function Type 2 poly-Bernoulli polynomial
Online Access:	http://link.springer.com/article/10.1186/s13662-020-03024-x

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spelling	doaj-366047499f894e6d8f76cf96fd59fb1a2020-11-25T03:37:06ZengSpringerOpenAdvances in Difference Equations1687-18472020-10-012020111310.1186/s13662-020-03024-xIdentities on poly-Dedekind sumsTaekyun Kim0Dae San Kim1Hyunseok Lee2Lee-Chae Jang3Department of Mathematics, Kwangwoon UniversityDepartment of Mathematics, Sogang UniversityDepartment of Mathematics, Kwangwoon UniversityGraduate School of Education, Konkuk UniversityAbstract 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.http://link.springer.com/article/10.1186/s13662-020-03024-xPoly-Dedekind sumPolyexponential functionType 2 poly-Bernoulli polynomial
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Taekyun Kim Dae San Kim Hyunseok Lee Lee-Chae Jang
spellingShingle	Taekyun Kim Dae San Kim Hyunseok Lee Lee-Chae Jang Identities on poly-Dedekind sums Advances in Difference Equations Poly-Dedekind sum Polyexponential function Type 2 poly-Bernoulli polynomial
author_facet	Taekyun Kim Dae San Kim Hyunseok Lee Lee-Chae Jang
author_sort	Taekyun Kim
title	Identities on poly-Dedekind sums
title_short	Identities on poly-Dedekind sums
title_full	Identities on poly-Dedekind sums
title_fullStr	Identities on poly-Dedekind sums
title_full_unstemmed	Identities on poly-Dedekind sums
title_sort	identities on poly-dedekind sums
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2020-10-01
description	Abstract 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.
topic	Poly-Dedekind sum Polyexponential function Type 2 poly-Bernoulli polynomial
url	http://link.springer.com/article/10.1186/s13662-020-03024-x
work_keys_str_mv	AT taekyunkim identitiesonpolydedekindsums AT daesankim identitiesonpolydedekindsums AT hyunseoklee identitiesonpolydedekindsums AT leechaejang identitiesonpolydedekindsums
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Identities on poly-Dedekind sums

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