Construction of Jacobi forms using adjoint of Jacobi-Serre derivative
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910287189245952 |
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| author | Charan, Mrityunjoy Vaishya, Lalit |
| author_facet | Charan, Mrityunjoy Vaishya, Lalit |
| contents | In the article, we study the Oberdieck derivative defined on the space of weak Jacobi forms. We prove that the Oberdieck derivative maps a Jacobi form to a Jacobi form. Moreover, we study the adjoint of Oberdieck derivative of a Jacobi cusp form with respect to Petersson scalar product defined on the space of Jacobi forms. As a consequence, we also obtain the adjoint of Jacobi-Serre derivative (defined in an unpublished work of Oberdieck). As an application, we obtain certain relations among the Fourier coefficients of Jacobi forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02182 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of Jacobi forms using adjoint of Jacobi-Serre derivative Charan, Mrityunjoy Vaishya, Lalit Number Theory Primary 11F50, 11F25 Secondary 11F30 In the article, we study the Oberdieck derivative defined on the space of weak Jacobi forms. We prove that the Oberdieck derivative maps a Jacobi form to a Jacobi form. Moreover, we study the adjoint of Oberdieck derivative of a Jacobi cusp form with respect to Petersson scalar product defined on the space of Jacobi forms. As a consequence, we also obtain the adjoint of Jacobi-Serre derivative (defined in an unpublished work of Oberdieck). As an application, we obtain certain relations among the Fourier coefficients of Jacobi forms. |
| title | Construction of Jacobi forms using adjoint of Jacobi-Serre derivative |
| topic | Number Theory Primary 11F50, 11F25 Secondary 11F30 |
| url | https://arxiv.org/abs/2401.02182 |