Arithmetic of generalized Dedekind sums and their modularity

Open Mathematics

Jun Byungheup¹  Lim Subong²  Choi Dohoon³  Lee Jungyun⁴ 

[1] Department of Mathematical Sciences, UNIST, UNIST-gil 50, Ulsan689-798, Republic of Korea;Department of Mathematics Education, Sungkyunkwan University, 25-2, Sungkyunkwan-ro, Jongno-gu, Seoul03063, Republic of Korea;Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul02841, Republic of Korea;Institute of Mathematical science, Ewha womans university, 11-1 Daehyun-Dong, Seodaemun-gu, Seoul, 120-750, Republic of Korea;

关键词: dedekind sum;    quantum modular form;    11f20;   

DOI  :  10.1515/math-2018-0082

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown