Generalized Dedekind sums and equidistribution mod 1

Dedekind sums are well-studied arithmetic sums, with values uniformly distributed mod 1. Based on their relation to certain modular forms, Dedekind sums may be defined as functions on the cusp set of SL(2,Z)SL(2,Z). We present a compatible notion of Dedekind sums, which we name Dedekind symbols, for any non-cocompact lattice Γ