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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.10681 |
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| _version_ | 1866909138309611520 |
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| author | Smoot, Nicolas Allen |
| author_facet | Smoot, Nicolas Allen |
| contents | Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary substantially in difficulty. Moreover, the critical difficulties associated with a given family will generally manifest themselves at the end stages of an attempted proof. We give a conjectured classification system of congruence families for the coefficients of modular eta quotients by studying the topology of the associated modular curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10681 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Classification of Modular Congruence Families Smoot, Nicolas Allen Number Theory Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary substantially in difficulty. Moreover, the critical difficulties associated with a given family will generally manifest themselves at the end stages of an attempted proof. We give a conjectured classification system of congruence families for the coefficients of modular eta quotients by studying the topology of the associated modular curve. |
| title | On the Classification of Modular Congruence Families |
| topic | Number Theory |
| url | https://arxiv.org/abs/2403.10681 |