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Bibliographic Details
Main Author: Smoot, Nicolas Allen
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2403.10681
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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.
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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