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arXiv · 2407.01368

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

Sebastián Herrero·Özlem Imamoglu·Anna-Maria von Pippich·Markus Schwagenscheidt
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Abstract

We compute analogues of twisted traces of CM values of harmonic modular functions on hyperbolic $3$-space and show that they are essentially given by Fourier coefficients of the $j$-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 $3$-space in terms of Dirichlet $L$-functions and divisor sums.

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Sebastián Herrero, Özlem Imamoglu, Anna-Maria von Pippich, Markus Schwagenscheidt. 2024-07-01. Twisted traces of modular functions on hyperbolic $3$-space. https://arxiv.org/abs/2407.01368

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