Arithmetic of generalized dedekind sums and their modularity

Dedekind sums were introduced by Dedekind to study the transformation properties of Dedekind ?? function under the action of SL2(???). In this paper, we study properties of generalized Dedekind sums si,j(p, q). We prove an asymptotic expansion of a function on ??? defined in terms of generalized Dedekind sums by using its modular property. We also prove an equidistribution property of generalized Dedekind sums