Rankin-Cohen Brackets of Hilbert Hecke Eigenforms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913366741614592 |
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| author | Zhang, Yichao Zhou, Yang |
| author_facet | Zhang, Yichao Zhou, Yang |
| contents | Over any fixed totally real number field with narrow class number one, we prove that the Rankin-Cohen bracket of two Hecke eigenforms for the Hilbert modular group can only be a Hecke eigenform for dimension reasons, except for a couple of cases where the Rankin-Selberg method does not apply. We shall also prove a conjecture of Freitag on the volume of Hilbert modular groups, and assuming a conjecture of Freitag on the dimension of the cuspform space, we obtain a finiteness result on eigenform product identities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17887 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rankin-Cohen Brackets of Hilbert Hecke Eigenforms Zhang, Yichao Zhou, Yang Number Theory Over any fixed totally real number field with narrow class number one, we prove that the Rankin-Cohen bracket of two Hecke eigenforms for the Hilbert modular group can only be a Hecke eigenform for dimension reasons, except for a couple of cases where the Rankin-Selberg method does not apply. We shall also prove a conjecture of Freitag on the volume of Hilbert modular groups, and assuming a conjecture of Freitag on the dimension of the cuspform space, we obtain a finiteness result on eigenform product identities. |
| title | Rankin-Cohen Brackets of Hilbert Hecke Eigenforms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2405.17887 |