On p-adic Siegel–Eisenstein Series II: How to Avoid the Regularity Condition for p

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2025年8月7日

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Siegfried Böcherer,
Toshiyuki Kikuta

摘要

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 $\Gamma _0(p)$ $Γ_{0} (p)$ , 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, $n\le 2k+1$ $n \leq 2 k + 1$ .