English

Transformation laws for generalized Dedekind sums associated to Fuchsian groups

Number Theory 2024-12-17 v1

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)\Gamma_0(N), and the non-congruence arithmetic groups Γ0(N)+\Gamma_0(N)^+.

Keywords

Cite

@article{arxiv.1904.11333,
  title  = {Transformation laws for generalized Dedekind sums associated to Fuchsian groups},
  author = {Claire Burrin and Jay Jorgenson and Cormac O'Sullivan and Lejla Smajlović},
  journal= {arXiv preprint arXiv:1904.11333},
  year   = {2024}
}

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18 pages