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arXiv · 2403.10681

On the Classification of Modular Congruence Families

Nicolas Allen Smoot
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Abstract

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.

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Nicolas Allen Smoot. 2024-03-15. On the Classification of Modular Congruence Families. https://arxiv.org/abs/2403.10681

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