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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/2208.01921 |
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| _version_ | 1866910695945142272 |
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| author | Müller, Manuel K. -H. Scheithauer, Nils R. |
| author_facet | Müller, Manuel K. -H. Scheithauer, Nils R. |
| contents | The transformation behaviour of the vector valued theta function of a positive-definite even lattice under the metaplectic group $\mathrm{Mp}_2(\mathbb{Z})$ is described by the Weil representation. We show that the invariants of this representation are induced from $5$ fundamental invariants. As an application we give simple generating sets for Jacobi forms of singular weight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_01921 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The invariants of the Weil representation of $\mathrm{SL}_2(\mathbb{Z})$ Müller, Manuel K. -H. Scheithauer, Nils R. Number Theory The transformation behaviour of the vector valued theta function of a positive-definite even lattice under the metaplectic group $\mathrm{Mp}_2(\mathbb{Z})$ is described by the Weil representation. We show that the invariants of this representation are induced from $5$ fundamental invariants. As an application we give simple generating sets for Jacobi forms of singular weight. |
| title | The invariants of the Weil representation of $\mathrm{SL}_2(\mathbb{Z})$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2208.01921 |