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arXiv · 2505.06956

On Siegel--Eisenstein series of level $p$ and their $p$-adic properties

Siegfried Boecherer·Keiichi Gunji·Toshiyuki Kikuta
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Abstract

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.

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Siegfried Boecherer, Keiichi Gunji, Toshiyuki Kikuta. 2025-05-11. On Siegel--Eisenstein series of level $p$ and their $p$-adic properties. https://arxiv.org/abs/2505.06956

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