On the partial derivatives of Drinfeld modular forms of arbitrary rank
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914576461725696 |
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| author | Chen, Yen-Tsung Gezmiş, Oğuz |
| author_facet | Chen, Yen-Tsung Gezmiş, Oğuz |
| contents | In this paper, we obtain an analogue of the Serre derivation acting on the product of spaces of Drinfeld modular forms which generalizes the differential operator introduced by Gekeler in the rank two case. We further introduce a finitely generated algebra $\mathcal{M}_r$ containing all the Drinfeld modular forms for the full modular group and show its stability under the partial derivatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_13997 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the partial derivatives of Drinfeld modular forms of arbitrary rank Chen, Yen-Tsung Gezmiş, Oğuz Number Theory 11F52 (Primary), 11G09 (Secondary) In this paper, we obtain an analogue of the Serre derivation acting on the product of spaces of Drinfeld modular forms which generalizes the differential operator introduced by Gekeler in the rank two case. We further introduce a finitely generated algebra $\mathcal{M}_r$ containing all the Drinfeld modular forms for the full modular group and show its stability under the partial derivatives. |
| title | On the partial derivatives of Drinfeld modular forms of arbitrary rank |
| topic | Number Theory 11F52 (Primary), 11G09 (Secondary) |
| url | https://arxiv.org/abs/2206.13997 |