Congruences for Siegel modular forms of nonquadratic nebentypus mod $p$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909093327798272 |
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| author | Boecherer, Siegfried Kikuta, Toshiyuki |
| author_facet | Boecherer, Siegfried Kikuta, Toshiyuki |
| contents | We prove that weights of two Siegel modular forms of nonquadratic nebentypus should satisfy some congruence relations if these modular forms are congruent to each other. Applying this result, we prove that there are no mod $p$ singular forms of nonquadratic nebentypus. Here we consider the case where the Fourier coefficients of the modular forms are algebraic integers, and we emphasize that $p$ is a rational prime. Moreover, we construct some examples of mod $\frak{p}$ singular forms of nonquadratic nebentypus using the Eisenstein series studied by Takemori. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02762 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Congruences for Siegel modular forms of nonquadratic nebentypus mod $p$ Boecherer, Siegfried Kikuta, Toshiyuki Number Theory Primary 11F33, Secondary 11F46 We prove that weights of two Siegel modular forms of nonquadratic nebentypus should satisfy some congruence relations if these modular forms are congruent to each other. Applying this result, we prove that there are no mod $p$ singular forms of nonquadratic nebentypus. Here we consider the case where the Fourier coefficients of the modular forms are algebraic integers, and we emphasize that $p$ is a rational prime. Moreover, we construct some examples of mod $\frak{p}$ singular forms of nonquadratic nebentypus using the Eisenstein series studied by Takemori. |
| title | Congruences for Siegel modular forms of nonquadratic nebentypus mod $p$ |
| topic | Number Theory Primary 11F33, Secondary 11F46 |
| url | https://arxiv.org/abs/2402.02762 |