منابع مشابه
Modular Forms for Noncongruence Subgroups
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...
متن کاملExperimental finding of modular forms for noncongruence subgroups
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.
متن کاملModular 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.
متن کاملModular Forms and Modular Symbols for Noncongruence Groups Table of Contents
Modular forms for congruence groups are a major area of research in number theory and have been studied extensively. Modular forms for noncongruence groups are less understood. In this thesis, we look at noncongruence groups from two points of view. The first is computational: We look at a method of computation with finite index subgroups of the modular group called Farey symbols. This method a...
متن کاملModular Towers of Noncongruence Curves
This proposal extends much work done during the last funding period. Two topics, however, which have separate goals, have brief summaries in x10. Together they form documentation of the results that came from the funding period of NSF GRANT #9622928. 1. An outline of the main problems of this proposal Let G be a nite group. Call a conjugacy class C a p 0-class if its elements have order prime t...
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ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2005
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2005.v1.n1.a9