On the Siegel series in terms of lattice counting
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909141861138432 |
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| author | Cho, Sungmun Kang, Taeyeoup |
| author_facet | Cho, Sungmun Kang, Taeyeoup |
| contents | In this paper we describe each coefficient of the Siegel series associated to a quadratic $\mathfrak{o}$-lattice $L$ in terms of lattice counting problems, where $\mathfrak{o}$ is the ring of integers of a non-Archimedean local field of characteristic $0$. Under the restriction that $p$ is odd and that the dimension of the radical of the quadratic space $L\otimesκ$ on the residue field $κ$ is at most $2$, we provide explicit values of coefficients and reprove the functional equation of the Siegel series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12476 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Siegel series in terms of lattice counting Cho, Sungmun Kang, Taeyeoup Number Theory 11E08, 11E45 (Primary) 11F30, 11E95 (Secondary) In this paper we describe each coefficient of the Siegel series associated to a quadratic $\mathfrak{o}$-lattice $L$ in terms of lattice counting problems, where $\mathfrak{o}$ is the ring of integers of a non-Archimedean local field of characteristic $0$. Under the restriction that $p$ is odd and that the dimension of the radical of the quadratic space $L\otimesκ$ on the residue field $κ$ is at most $2$, we provide explicit values of coefficients and reprove the functional equation of the Siegel series. |
| title | On the Siegel series in terms of lattice counting |
| topic | Number Theory 11E08, 11E45 (Primary) 11F30, 11E95 (Secondary) |
| url | https://arxiv.org/abs/2403.12476 |