On Rankin-Cohen Brackets of Hecke Eigenforms and Modular Forms of Half-Integral Weight
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916261527552000 |
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| author | Choie, YoungJu Kohnen, Winfried Zhang, Yichao |
| author_facet | Choie, YoungJu Kohnen, Winfried Zhang, Yichao |
| contents | We generalize the linear relation formula between the square of normalized Hecke eigenforms of weight $k$ and normalized Hecke eigenforms of weight $2k$, to Rankin-Cohen brackets of general degree. As an ingredient of the proof, we also generalize a formula of Zagier on the Petersson inner product of Rankin-Cohen brackets involving Eisenstein series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16745 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Rankin-Cohen Brackets of Hecke Eigenforms and Modular Forms of Half-Integral Weight Choie, YoungJu Kohnen, Winfried Zhang, Yichao Number Theory 11F11, 11F37, 11F25 We generalize the linear relation formula between the square of normalized Hecke eigenforms of weight $k$ and normalized Hecke eigenforms of weight $2k$, to Rankin-Cohen brackets of general degree. As an ingredient of the proof, we also generalize a formula of Zagier on the Petersson inner product of Rankin-Cohen brackets involving Eisenstein series. |
| title | On Rankin-Cohen Brackets of Hecke Eigenforms and Modular Forms of Half-Integral Weight |
| topic | Number Theory 11F11, 11F37, 11F25 |
| url | https://arxiv.org/abs/2405.16745 |