Rankin-Cohen Bracket for Vector-Valued Modular Forms
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909994533781504 |
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| author | Lee, Youngmin Lim, Subong Raji, Wissam |
| author_facet | Lee, Youngmin Lim, Subong Raji, Wissam |
| contents | In this paper, we explore the relationship between Rankin-Cohen brackets for vector-valued modular forms and Petersson's inner products, deriving an explicit description of the adjoint map for the bracket operator. The study extends to the cases of Jacobi forms and skew-holomorphic Jacobi forms, establishing connections between their respective Rankin-Cohen brackets and those defined for vector-valued modular forms through an isomorphism. Adjoint maps for these extended bracket operators are also examined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12860 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rankin-Cohen Bracket for Vector-Valued Modular Forms Lee, Youngmin Lim, Subong Raji, Wissam Number Theory 11F11, 11FXX In this paper, we explore the relationship between Rankin-Cohen brackets for vector-valued modular forms and Petersson's inner products, deriving an explicit description of the adjoint map for the bracket operator. The study extends to the cases of Jacobi forms and skew-holomorphic Jacobi forms, establishing connections between their respective Rankin-Cohen brackets and those defined for vector-valued modular forms through an isomorphism. Adjoint maps for these extended bracket operators are also examined. |
| title | Rankin-Cohen Bracket for Vector-Valued Modular Forms |
| topic | Number Theory 11F11, 11FXX |
| url | https://arxiv.org/abs/2601.12860 |