Twisted traces of modular functions on hyperbolic $3$-space
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909236471005184 |
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| author | Herrero, Sebastián Imamoglu, Özlem von Pippich, Anna-Maria Schwagenscheidt, Markus |
| author_facet | Herrero, Sebastián Imamoglu, Özlem von Pippich, Anna-Maria Schwagenscheidt, Markus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted traces of modular functions on hyperbolic $3$-space Herrero, Sebastián Imamoglu, Özlem von Pippich, Anna-Maria Schwagenscheidt, Markus Number Theory 11F55, 11F37 (primary), 11F30 (secondary) 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. |
| title | Twisted traces of modular functions on hyperbolic $3$-space |
| topic | Number Theory 11F55, 11F37 (primary), 11F30 (secondary) |
| url | https://arxiv.org/abs/2407.01368 |