Finite index subgroups of the modular group and their modular forms

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dc.creatorLong, Ling
dc.date2007-07-23
dc.date.accessioned2026-07-07T08:19:40Z
dc.date.available2026-07-07T08:19:40Z
dc.descriptionClassically, congruence subgroups of the modular group, which can be described by congruence relations, play important roles in group theory and modular forms. In reality, the majority of finite index subgroups of the modular group are noncongruence. These groups as well as their modular forms are central players of this survey article. Differences between congruence and noncongruence subgroups and modular forms will be discussed. We will mainly focus on three interesting aspects of modular forms for noncongruence subgroups: the unbounded denominator property, modularity of the Galois representation arising from noncongruence cuspforms, and Atkin and Swinnerton-Dyer congruences.
dc.descriptionA survey article
dc.identifierhttps://arxiv.org/abs/0707.3315
dc.identifierhttp://arxiv.org/abs/0707.3315
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134841
dc.subjectNumber Theory
dc.subject11F11
dc.titleFinite index subgroups of the modular group and their modular forms
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