Explicit Hecke eigenform product identities for Hilbert modular forms
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866918374708084736 |
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| author | Hao, Zeping Qin, Chao Zhou, Yang |
| author_facet | Hao, Zeping Qin, Chao Zhou, Yang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03071 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit Hecke eigenform product identities for Hilbert modular forms Hao, Zeping Qin, Chao Zhou, Yang Number Theory 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. |
| title | Explicit Hecke eigenform product identities for Hilbert modular forms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2508.03071 |