English

Twisted traces of modular functions on hyperbolic $3$-space

Number Theory 2024-07-02 v1

Abstract

We compute analogues of twisted traces of CM values of harmonic modular functions on hyperbolic 33-space and show that they are essentially given by Fourier coefficients of the jj-invariant. From this we deduce that the twisted traces of these harmonic modular functions are integers. Additionally, we compute the twisted traces of Eisenstein series on hyperbolic 33-space in terms of Dirichlet LL-functions and divisor sums.

Keywords

Cite

@article{arxiv.2407.01368,
  title  = {Twisted traces of modular functions on hyperbolic $3$-space},
  author = {Sebastián Herrero and Özlem Imamoglu and Anna-Maria von Pippich and Markus Schwagenscheidt},
  journal= {arXiv preprint arXiv:2407.01368},
  year   = {2024}
}
R2 v1 2026-06-28T17:25:05.917Z