On Siegel--Eisenstein series of level $p$ and their $p$-adic properties
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908359984152576 |
|---|---|
| author | Boecherer, Siegfried Gunji, Keiichi Kikuta, Toshiyuki |
| author_facet | Boecherer, Siegfried Gunji, Keiichi Kikuta, Toshiyuki |
| contents | We construct a Siegel--Eisenstein series of level $p$ with a quadratic character mod $p$ which is a $U(p)$-eigenfunction with eigenvalue $1$, and calculate its Fourier coefficients explicitly. We show that this Siegel--Eisenstein series is a $p$-adic Siegel--Eisenstein series, i.e., it is a $p$-adic limit of a sequence of Siegel--Eisenstein series of level $1$. We prove also that the Siegel--Eisenstein series with a nonquadratic character mod $p$ constructed by Takemori is also a $p$-adic Siegel--Eisenstein series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Siegel--Eisenstein series of level $p$ and their $p$-adic properties Boecherer, Siegfried Gunji, Keiichi Kikuta, Toshiyuki Number Theory 11F33, 11F46 We construct a Siegel--Eisenstein series of level $p$ with a quadratic character mod $p$ which is a $U(p)$-eigenfunction with eigenvalue $1$, and calculate its Fourier coefficients explicitly. We show that this Siegel--Eisenstein series is a $p$-adic Siegel--Eisenstein series, i.e., it is a $p$-adic limit of a sequence of Siegel--Eisenstein series of level $1$. We prove also that the Siegel--Eisenstein series with a nonquadratic character mod $p$ constructed by Takemori is also a $p$-adic Siegel--Eisenstein series. |
| title | On Siegel--Eisenstein series of level $p$ and their $p$-adic properties |
| topic | Number Theory 11F33, 11F46 |
| url | https://arxiv.org/abs/2505.06956 |