Modular Forms on Noncongruence Subgroups and Atkin–Swinnerton-Dyer Relations
نویسندگان
چکیده
منابع مشابه
Modular Forms on Noncongruence Subgroups and Atkin-Swinnerton-Dyer Relations
This is a joint project with Liqun Fang Ben Linowitz Andrew Rupinski Helena Verrill We give new examples of modular forms on noncongruence subgroups whose l-adic representations are modular and whose expansion coefficients satisfy Atkin-Swinnerton-Dyer congruences.
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The study of modular forms for congruence subgroups of SL2(Z) has been one of the central topics in number theory for over one century. It has broad applications and impact to many branches of mathematics. Langlands’ program is a vast generalization of this subject from representation-theoretic point of view. The most recent highlight is the proof of the Taniyama-Shimura-Weil modularity conject...
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In this paper we will use experimental and computational methods to find modular forms for non-congruence subgroups, and the modular forms for congruence subgroups that they are associated with via the Atkin–Swinnerton-Dyer correspondence. We also prove a generalization of a criterion due to Ligozat for an eta-quotient to be a modular function.
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Arithmetic subgroups are finite index subgroups of the modular group. Classically, congruence arithmetic subgroups, which can be described by congruence relations, are playing important roles in group theory and modular forms. In reality, the majority of arithmetic subgroups are noncongruence. These groups as well as their modular forms are central players of this survey article. Differences be...
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Classically, 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...
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ژورنال
عنوان ژورنال: Experimental Mathematics
سال: 2010
ISSN: 1058-6458,1944-950X
DOI: 10.1080/10586458.2010.10129064