Ramanujan type congruences for the Klingen-Eisenstein series

2014/02/13 by Toshiyuki Kikuta, Sho Takemori, Kikuta, Toshiyuki +1
Mathematics · #11F33 #11F46 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1402.3159

openalex publication_date 2014/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the case of Siegel modular forms of degree n, we prove that, for almost all prime ideals \frakp in any ring of algebraic integers, mod \frakp^m cusp forms are congruent to true cusp forms of the same weight. As an application of this property, we give congruences for the Klingen-Eisenstein series and cusp forms, which can be regarded as a generalization of Ramanujan's congruence. We will conclude by giving numerical examples.

Related

• Ramanujan type congruences for modular forms of several variables
• Ramanujan-style congruences for prime level
• Relations among Ramanujan-Type Congruences I
• Klingen Eisenstein series congruences and modularity
• On mod p singular modular forms