Rigorous expansions of modular forms at CM points, I: Denominators
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915132672573440 |
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| author | Xu, Chris |
| author_facet | Xu, Chris |
| contents | We describe an algorithm to rigorously compute the power series expansion at a CM point of a weight $2$ cusp form of level coprime to $6$. Our algorithm works by bounding the denominators that appear due to ramification, and without recourse to computing an explicit model of the corresponding modular curve. Our result is the first in a series of papers toward an eventual implementation of equationless Chabauty. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00326 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigorous expansions of modular forms at CM points, I: Denominators Xu, Chris Number Theory Algebraic Geometry We describe an algorithm to rigorously compute the power series expansion at a CM point of a weight $2$ cusp form of level coprime to $6$. Our algorithm works by bounding the denominators that appear due to ramification, and without recourse to computing an explicit model of the corresponding modular curve. Our result is the first in a series of papers toward an eventual implementation of equationless Chabauty. |
| title | Rigorous expansions of modular forms at CM points, I: Denominators |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2502.00326 |