On a Divisor Modular Form and a Theta Lift
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912563777765376 |
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| author | Mono, Andreas Rolen, Larry Stumpenhusen, Johann |
| author_facet | Mono, Andreas Rolen, Larry Stumpenhusen, Johann |
| contents | In 1975, Zagier introduced the highly influential hyperbolic Poincaré series $f_{k,D}$. We connect the divisor modular form of $f_{k,D}$ to a new weak Maass form $ω_{k+1,D}$. Furthermore, we show that the generating function of $ω_{k+1,D}$ has the same modularity properties as Kohnen and Zagier's fruitful theta kernel generating the $f_{k,D}$'s. This yields a new theta lift. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01378 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a Divisor Modular Form and a Theta Lift Mono, Andreas Rolen, Larry Stumpenhusen, Johann Number Theory In 1975, Zagier introduced the highly influential hyperbolic Poincaré series $f_{k,D}$. We connect the divisor modular form of $f_{k,D}$ to a new weak Maass form $ω_{k+1,D}$. Furthermore, we show that the generating function of $ω_{k+1,D}$ has the same modularity properties as Kohnen and Zagier's fruitful theta kernel generating the $f_{k,D}$'s. This yields a new theta lift. |
| title | On a Divisor Modular Form and a Theta Lift |
| topic | Number Theory |
| url | https://arxiv.org/abs/2509.01378 |