Claire Burrin, Jay Jorgenson, Cormac O'Sullivan, Lejla Smajlović
Published 2019-04-25Version 1
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 $\Gamma_0(N)^+$.
Generalized Dedekind sums and equidistribution mod 1
Eigenfunctions of transfer operators and automorphic forms for Hecke triangle groups of infinite covolume
An analogue of the Rademacher function for generalized Dedekind sums in higher dimension
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