Drinfeld Quasi-Modular Forms of Higher Level
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912705715109888 |
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| author | Bandini, Andrea Valentino, Maria de Vries, Sjoerd |
| author_facet | Bandini, Andrea Valentino, Maria de Vries, Sjoerd |
| contents | We study the structure of the vector space of Drinfeld quasi-modular forms for congruence subgroups. We provide representations as polynomials in the false Eisenstein series with coefficients in the space of Drinfeld modular forms (the $E$-expansion), and, whenever possible, as sums of hyperderivatives of Drinfeld modular forms. \\ Moreover, we introduce and study the double-slash operator, and use it to provide a well-posed definition for Hecke operators on Drinfeld quasi-modular forms. We characterize eigenforms and, for the special case of Hecke congruence subgroups $Γ_0(\mathfrak n)$, we give explicit formulas for the Hecke action on $E$-expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08263 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Drinfeld Quasi-Modular Forms of Higher Level Bandini, Andrea Valentino, Maria de Vries, Sjoerd Number Theory 11F52, 11F25 We study the structure of the vector space of Drinfeld quasi-modular forms for congruence subgroups. We provide representations as polynomials in the false Eisenstein series with coefficients in the space of Drinfeld modular forms (the $E$-expansion), and, whenever possible, as sums of hyperderivatives of Drinfeld modular forms. \\ Moreover, we introduce and study the double-slash operator, and use it to provide a well-posed definition for Hecke operators on Drinfeld quasi-modular forms. We characterize eigenforms and, for the special case of Hecke congruence subgroups $Γ_0(\mathfrak n)$, we give explicit formulas for the Hecke action on $E$-expansions. |
| title | Drinfeld Quasi-Modular Forms of Higher Level |
| topic | Number Theory 11F52, 11F25 |
| url | https://arxiv.org/abs/2502.08263 |