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arXiv · 2508.03071

Explicit Hecke eigenform product identities for Hilbert modular forms

Zeping Hao·Chao Qin·Yang Zhou
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Abstract

Let $F$ be a totally real number field, and $g,f,h$ be Hilbert modular forms over $F$ that are Hecke eigenforms satisfying $g=f\cdot h$. We characterize such product identities among all real quadratic fields of narrow class number one, proving they occur only for $F=\mathbb Q(\sqrt{5})$, 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.

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Zeping Hao, Chao Qin, Yang Zhou. 2025-08-05. Explicit Hecke eigenform product identities for Hilbert modular forms. https://arxiv.org/abs/2508.03071

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