Locally harmonic Maaß forms of positive even weight
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866915738423394304 |
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| author | Mono, Andreas |
| author_facet | Mono, Andreas |
| contents | We twist Zagier's function $f_{k,D}$ by a sign function and a genus character. Assuming weight $0 < k \equiv 2 \pmod{4}$, and letting $D$ be a positive non-square discriminant, we prove that the obstruction to modularity caused by the sign function can be corrected obtaining a locally harmonic Maaßform or a local cusp form of the same weight. In addition, we provide an alternative representation of our new function in terms of a twisted trace of modular cycle integrals of a Poincaré series due to Petersson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_03127 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Locally harmonic Maaß forms of positive even weight Mono, Andreas Number Theory 11F12 (Primary), 11E16, 11E45, 11F37 (Secondary) We twist Zagier's function $f_{k,D}$ by a sign function and a genus character. Assuming weight $0 < k \equiv 2 \pmod{4}$, and letting $D$ be a positive non-square discriminant, we prove that the obstruction to modularity caused by the sign function can be corrected obtaining a locally harmonic Maaßform or a local cusp form of the same weight. In addition, we provide an alternative representation of our new function in terms of a twisted trace of modular cycle integrals of a Poincaré series due to Petersson. |
| title | Locally harmonic Maaß forms of positive even weight |
| topic | Number Theory 11F12 (Primary), 11E16, 11E45, 11F37 (Secondary) |
| url | https://arxiv.org/abs/2104.03127 |