Recursion formulas for the Fourier coefficients of Siegel Eisenstein series of an odd prime level
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913806620295168 |
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| author | Gunji, Keiichi |
| author_facet | Gunji, Keiichi |
| contents | In this paper we treat the Fourier coefficients of Siegel Eisenstein series of level $p$ with trivial or quadratic character, for an odd prime $p$. The Euler $p$-factor of the Fourier coefficient is called the ramified Siegel series. First we show that the ramified Siegel series attached to each cusp can be decomposed to $U(p)$-eigenfunctions explicitly, next we give recursion formulas of such $U(p)$-characteristic ramified Siegel series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17245 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Recursion formulas for the Fourier coefficients of Siegel Eisenstein series of an odd prime level Gunji, Keiichi Number Theory 11F30 (Primary), 11F46(Secondary) In this paper we treat the Fourier coefficients of Siegel Eisenstein series of level $p$ with trivial or quadratic character, for an odd prime $p$. The Euler $p$-factor of the Fourier coefficient is called the ramified Siegel series. First we show that the ramified Siegel series attached to each cusp can be decomposed to $U(p)$-eigenfunctions explicitly, next we give recursion formulas of such $U(p)$-characteristic ramified Siegel series. |
| title | Recursion formulas for the Fourier coefficients of Siegel Eisenstein series of an odd prime level |
| topic | Number Theory 11F30 (Primary), 11F46(Secondary) |
| url | https://arxiv.org/abs/2504.17245 |