On $p$-adic Siegel--Eisenstein series II: How to avoid the regularity condition for $p$

Siegfried Boecherer; Toshiyuki Kikuta

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arXiv · 2502.06799

On $p$-adic Siegel--Eisenstein series II: How to avoid the regularity condition for $p$

Siegfried Boecherer·Toshiyuki Kikuta

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Abstract

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 $\Gamma _0(p)$, 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, $n\le 2k+1$.

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Siegfried Boecherer, Toshiyuki Kikuta. 2025-01-29. On $p$-adic Siegel--Eisenstein series II: How to avoid the regularity condition for $p$. https://arxiv.org/abs/2502.06799

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