The equidistribution of elliptic Dedekind sums and generalized Selberg–Kloosterman sums

We show that the values of elliptic Dedekind sums, after normalization, are equidistributed mod 1. The key ingredient is a non-trivial bound on generalized Selberg–Kloosterman sums for discrete subgroups of \(\textrm{PSL}_2({\mathbb {C}})\) ${\text{PSL}}_2(\mathbb{C})$ using Poincaré series.