Transformation laws for generalized Dedekind sums associated to Fuchsian groups
Volume 196 / 2020
Acta Arithmetica 196 (2020), 139-162
MSC: 11F20, 30F35.
DOI: 10.4064/aa190425-31-1
Published online: 19 June 2020
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 $\Gamma _0(N)^+$.
