Arithmetic of generalized dedekind sums and their modularity

Dohoon Choi, Byungheup Jun, Jungyun Lee, Subong Lim

Research output: Contribution to journalArticlepeer-review

Abstract

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 ℚdefined in terms of generalized Dedekind sums by using its modular property. We also prove an equidistribution property of generalized Dedekind sums.

Original languageEnglish
Pages (from-to)967-985
Number of pages19
JournalOpen Mathematics
Volume16
Issue number1
DOIs
Publication statusPublished - 2018

Bibliographical note

Funding Information:
The second named author was supported by (NRF-2015R1D1A1A09059083)

Funding Information:
The second named author was supported by (NRF-2015R1D1A1A09059083) and the third named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827) and (NRF-2017R1A6A3A11030486) and the last author was supported by (NRF-2017R1C1B5017409).

Publisher Copyright:
© 2018 Choi et al., published by De Gruyter. 2018.

Keywords

  • Dedekind sum
  • Quantum modular form

ASJC Scopus subject areas

  • General Mathematics

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