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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.07341 |
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| _version_ | 1866913685332557824 |
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| author | Ehlen, Stephan Li, Yingkun Schwagenscheidt, Markus |
| author_facet | Ehlen, Stephan Li, Yingkun Schwagenscheidt, Markus |
| contents | In this paper, we use a regularized theta lifting to construct harmonic Maass forms corresponding to binary theta functions of weight $k \ge 2$ under the $ξ$-operator. As a result, we show that their holomorphic parts have algebraic Fourier coefficients, with compatible Galois action. As an application, we prove rationality properties of coefficients of harmonic Maaass forms corresponding to CM newforms, answering a question of Bruinier, Ono and Rhoades. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_07341 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Harmonic Maass forms associated with CM newforms Ehlen, Stephan Li, Yingkun Schwagenscheidt, Markus Number Theory In this paper, we use a regularized theta lifting to construct harmonic Maass forms corresponding to binary theta functions of weight $k \ge 2$ under the $ξ$-operator. As a result, we show that their holomorphic parts have algebraic Fourier coefficients, with compatible Galois action. As an application, we prove rationality properties of coefficients of harmonic Maaass forms corresponding to CM newforms, answering a question of Bruinier, Ono and Rhoades. |
| title | Harmonic Maass forms associated with CM newforms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2210.07341 |