Transformation laws for generalized Dedekind sums associated to Fuchsian groups

Abstract

We establish transformation laws for generalized Dedekind sums associated to the Kronecker limit function of non-holomorphic Eisenstein series and their higher-order variants. These results apply to general Fuchsian groups of the first kind, and examples are provided in the cases of the Hecke triangle groups, the Hecke congruence groups ${\Gamma }_0(N)$, and the non-congruence arithmetic groups ${\Gamma }_0(N{)}^{+}$.

18 pages

References in corpus (2)

• Generalized Dedekind sums and equidistribution mod 1
• Reciprocity of Dedekind sums and the Euler class