Generating Picard modular forms by means of invariant theory
| Autor: | Cléry, Fabien, van der Geer, Gerard |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We use the description of the Picard modular surface for discriminant $-3$ as a moduli space of curves of genus $3$ to generate all vector-valued Picard modular forms from bi-covariants for the action of ${GL}_2$ on the space of pairs of binary forms of bidegree $(4,1)$. The universal binary forms of degree $4$ and $1$ correspond to a meromorphic modular form of weight $(4,-2)$ and a holomorphic Eisenstein series of weight $(1,1)$. Comment: 41 pages; minor changes. To appear in PAMQ |
| Databáze: | arXiv |
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