Experimental 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 Ligoza...

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Bibliographic Details
Published in:arXiv.org 2009-10
Main Author: Kilford, L J P
Format: Article
Language:English
Subjects:
Analytic functions
Subgroups
Online Access:Get full text
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Summary: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.
ISSN:2331-8422