Congruences for Siegel modular forms of nonquadratic nebentypus mod p

2024/02/05 by Siegfried Boecherer, Boecherer, Siegfried, Toshiyuki Kikuta +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Primary 11F33 #Secondary 11F46

paper · pdf · doi:10.48550/arxiv.2402.02762

openalex publication_date 2024/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that weights of two Siegel modular forms of nonquadratic nebentypus should satisfy some congruence relations if these modular forms are congruent to each other. Applying this result, we prove that there are no mod p singular forms of nonquadratic nebentypus. Here we consider the case where the Fourier coefficients of the modular forms are algebraic integers, and we emphasize that p is a rational prime. Moreover, we construct some examples of mod \frakp singular forms of nonquadratic nebentypus using the Eisenstein series studied by Takemori.

Related

• The structure of Siegel modular forms modulo p and U(p) congruences
• Structure theorem for mod p^m singular Siegel modular forms
• Sturm type theorem for Siegel modular forms of degree 2
• On mod p singular modular forms
• On p-adic Siegel modular forms of non-real Nebentypus of degree 2