On $p$-adic Siegel--Eisenstein series II: How to avoid the regularity condition for $p$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916606716674048 |
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| author | Boecherer, Siegfried Kikuta, Toshiyuki |
| author_facet | Boecherer, Siegfried Kikuta, Toshiyuki |
| contents | In a previous paper, the authors showed that two kinds of $p$-adic Siegel--Eisenstein series of degree $n$ coincide with classical modular forms of weight $k$ for $Γ_0(p)$, under the assumption that $p$ is a regular prime. The purpose of this paper is to show that this condition on $p$ can be removed if the degree $n$ is low compared with $k$, namely, $n\le 2k+1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_06799 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On $p$-adic Siegel--Eisenstein series II: How to avoid the regularity condition for $p$ Boecherer, Siegfried Kikuta, Toshiyuki Number Theory 11F33, 11F46 In a previous paper, the authors showed that two kinds of $p$-adic Siegel--Eisenstein series of degree $n$ coincide with classical modular forms of weight $k$ for $Γ_0(p)$, under the assumption that $p$ is a regular prime. The purpose of this paper is to show that this condition on $p$ can be removed if the degree $n$ is low compared with $k$, namely, $n\le 2k+1$. |
| title | On $p$-adic Siegel--Eisenstein series II: How to avoid the regularity condition for $p$ |
| topic | Number Theory 11F33, 11F46 |
| url | https://arxiv.org/abs/2502.06799 |