Arithmetic of generalized Dedekind sums and their modularity

Arithmetic of generalized Dedekind sums and their modularity

Dedekind sums were introduced by Dedekind to study the transformation properties of Dedekind η function under the action of SL2(ℤ). In this paper, we study properties of generalized Dedekind sums si,j(p, q). We prove an asymptotic expansion of a function on ℚ defined in terms of generalized Dedekind...

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Main Authors: Choi Dohoon, Jun Byungheup, Lee Jungyun, Lim Subong
Format: Article
Language:English
Published: De Gruyter 2018-09-01
Series:Open Mathematics
Subjects:
dedekind sum
quantum modular form
11f20
Online Access:https://doi.org/10.1515/math-2018-0082
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spelling doaj-d1b3bc913cea45d2b6799104d456eb042021-09-06T19:20:10ZengDe GruyterOpen Mathematics2391-54552018-09-0116196798510.1515/math-2018-0082math-2018-0082Arithmetic of generalized Dedekind sums and their modularityChoi Dohoon0Jun Byungheup1Lee Jungyun2Lim Subong3Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul02841, Republic of KoreaDepartment of Mathematical Sciences, UNIST, UNIST-gil 50, Ulsan689-798, Republic of KoreaInstitute of Mathematical science, Ewha womans university, 11-1 Daehyun-Dong, Seodaemun-gu, Seoul, 120-750, Republic of KoreaDepartment of Mathematics Education, Sungkyunkwan University, 25-2, Sungkyunkwan-ro, Jongno-gu, Seoul03063, Republic of KoreaDedekind sums were introduced by Dedekind to study the transformation properties of Dedekind η function under the action of SL2(ℤ). In this paper, we study properties of generalized Dedekind sums si,j(p, q). We prove an asymptotic expansion of a function on ℚ defined in terms of generalized Dedekind sums by using its modular property. We also prove an equidistribution property of generalized Dedekind sums.https://doi.org/10.1515/math-2018-0082dedekind sumquantum modular form11f20
collection DOAJ
language English
format Article
sources DOAJ
author Choi Dohoon
Jun Byungheup
Lee Jungyun
Lim Subong
spellingShingle Choi Dohoon
Jun Byungheup
Lee Jungyun
Lim Subong
Arithmetic of generalized Dedekind sums and their modularity
Open Mathematics
dedekind sum
quantum modular form
11f20
author_facet Choi Dohoon
Jun Byungheup
Lee Jungyun
Lim Subong
author_sort Choi Dohoon
title Arithmetic of generalized Dedekind sums and their modularity
title_short Arithmetic of generalized Dedekind sums and their modularity
title_full Arithmetic of generalized Dedekind sums and their modularity
title_fullStr Arithmetic of generalized Dedekind sums and their modularity
title_full_unstemmed Arithmetic of generalized Dedekind sums and their modularity
title_sort arithmetic of generalized dedekind sums and their modularity
publisher De Gruyter
series Open Mathematics
issn 2391-5455
publishDate 2018-09-01
description Dedekind sums were introduced by Dedekind to study the transformation properties of Dedekind η function under the action of SL2(ℤ). In this paper, we study properties of generalized Dedekind sums si,j(p, q). We prove an asymptotic expansion of a function on ℚ defined in terms of generalized Dedekind sums by using its modular property. We also prove an equidistribution property of generalized Dedekind sums.
topic dedekind sum
quantum modular form
11f20
url https://doi.org/10.1515/math-2018-0082
work_keys_str_mv AT choidohoon arithmeticofgeneralizeddedekindsumsandtheirmodularity
AT junbyungheup arithmeticofgeneralizeddedekindsumsandtheirmodularity
AT leejungyun arithmeticofgeneralizeddedekindsumsandtheirmodularity
AT limsubong arithmeticofgeneralizeddedekindsumsandtheirmodularity
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