Twisted traces of modular functions on hyperbolic \(3\)-space

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. Additiona...

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Authors: Herrero, Sebastián, Imamoglu, Özlem, Anna-Maria von Pippich, Schwagenscheidt, Markus
Format: Article
Language:English
Subjects:
Dirichlet problem
Harmonic functions
Online Access:Get full text
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Summary: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.
ISSN:2331-8422