Note on mod p property of Hermitian modular forms

2016/01/14 by Toshiyuki Kikuta, Kikuta, Toshiyuki, Shōyū Nagaoka +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1601.03506

openalex publication_date 2016/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The mod p kernel of the theta operator is the set of modular forms whose image of the theta operator is congruent to zero modulo a prime p. In the case of Siegel modular forms, the authors found interesting examples of such modular forms. For example, Igusa's odd weight cusp form is an element of mod 23 kernel of the theta operator. In this paper, we give some examples which represent elements in the mod p kernel of the theta operator in the case of Hermitian modular forms of degree 2.

Citations

• On mod p singular modular forms
• Weights of the mod p kernel of the theta operators

Related

• On the mod p kernel of the theta operator and Eisenstein series
• On the kernel of the theta operator mod p
• Theta operator for Hermitian modular forms over the Eisenstein field
• Weights of the mod p kernel of the theta operators
• The weight reduction of mod p Siegel modular forms for GSp₄