Certain Siegel Cusp Forms with Level are Determined by their Fundamental Fourier Coefficients
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911105138294784 |
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| author | Washburn, Sidney |
| author_facet | Washburn, Sidney |
| contents | We prove that vector-valued Siegel cusp forms for $Γ_0^n(N)$ with certain nebentypus are determined by their fundamental Fourier coefficients with discriminants coprime to the level $N$, assuming $N$ is odd and square-free. In the case of genus $3$, we strengthen this to Fourier coefficients corresponding to maximal orders in quaternion algebras. We also prove that Jacobi forms of fundamental index with discriminant coprime to the odd level $N$ are determined by their primitive theta components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17002 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Certain Siegel Cusp Forms with Level are Determined by their Fundamental Fourier Coefficients Washburn, Sidney Number Theory 11F46, 11F30 (Primary) 11F50 (Secondary) We prove that vector-valued Siegel cusp forms for $Γ_0^n(N)$ with certain nebentypus are determined by their fundamental Fourier coefficients with discriminants coprime to the level $N$, assuming $N$ is odd and square-free. In the case of genus $3$, we strengthen this to Fourier coefficients corresponding to maximal orders in quaternion algebras. We also prove that Jacobi forms of fundamental index with discriminant coprime to the odd level $N$ are determined by their primitive theta components. |
| title | Certain Siegel Cusp Forms with Level are Determined by their Fundamental Fourier Coefficients |
| topic | Number Theory 11F46, 11F30 (Primary) 11F50 (Secondary) |
| url | https://arxiv.org/abs/2507.17002 |