Arithmetic of generalized dedekind sums and their modularity

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. © 2018 Choi et al., published by De Gruyter. 2018.