Explicit Hecke eigenform product identities for Hilbert modular forms

2025/08/05 by Hao, Zeping, Qin, Chao, Zhou, Yang
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.03071

Abstract

Let F be a totally real number field, and g,f,h be Hilbert modular forms over F that are Hecke eigenforms satisfying g=f⋅ h. We characterize such product identities among all real quadratic fields of narrow class number one, proving they occur only for F=\mathbb Q(√(5)), with precisely two such identities. We also shed some light on the general totally real case by showing that no such identity exists when both f and h are Eisenstein series of distinct weights.

Citations

• Rankin-Cohen Brackets of Hilbert Hecke Eigenforms
• Hecke Eigenforms as Products of Eigenforms
• Enumeration of totally real number fields of bounded root discriminant

Related

• Rankin-Cohen Brackets of Hilbert Hecke Eigenforms
• Explicit methods for Hilbert modular forms
• Hecke Eigenforms as Products of Eigenforms
• Hilbert modular Eisenstein congruences of local origin
• Hecke and Sturm bounds for Hilbert modular forms over real quadratic fields