Arithmetic of generalized dedekind sums and their modularity

Dohoon Choi, Byungheup Jun, Jungyun Lee, Subong Lim

Research output: Contribution to journalArticle

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 Jan 1
Externally publishedYes

Keywords

  • Dedekind sum
  • Quantum modular form

ASJC Scopus subject areas

  • Mathematics(all)

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