On p-adic properties of Siegel modular forms

2013/05/03 by Siegfried Boecherer, Boecherer, Siegfried, Shōyū Nagaoka +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1305.0604

openalex publication_date 2013/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that Siegel modular forms of level Γ₀(p^m) are p-adic modular forms. Moreover we show that derivatives of such Siegel modular forms are p-adic. Parts of our results are also valid for vector-valued modular forms. In our approach to p-adic Siegel modular forms we follow Serre closely; his proofs however do not generalize to the Siegel case or need some modifications.

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