Transformation laws for modular Dedekind symbols

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 Γ0(N), and the non-congruence arithmetic groups Γ0(N)+.