On $p$-adic Siegel Eisenstein series from a point of view of the theory of mod $p^m$ singular forms
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910310622822400 |
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| author | Boecherer, Siegfried Kikuta, Toshiyuki |
| author_facet | Boecherer, Siegfried Kikuta, Toshiyuki |
| contents | We show that the $p$-adic Siegel Eisenstein series of general degree attached to two kind of number sequences are both linear combinations of genus theta series of level $p$, by applying the theory of mod $p$-power singular forms. As special cases of this result, we derive the result of Nagaoka and Katsurada--Nagaoka. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_03578 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On $p$-adic Siegel Eisenstein series from a point of view of the theory of mod $p^m$ singular forms Boecherer, Siegfried Kikuta, Toshiyuki Number Theory 11F33, 11F46 We show that the $p$-adic Siegel Eisenstein series of general degree attached to two kind of number sequences are both linear combinations of genus theta series of level $p$, by applying the theory of mod $p$-power singular forms. As special cases of this result, we derive the result of Nagaoka and Katsurada--Nagaoka. |
| title | On $p$-adic Siegel Eisenstein series from a point of view of the theory of mod $p^m$ singular forms |
| topic | Number Theory 11F33, 11F46 |
| url | https://arxiv.org/abs/2306.03578 |