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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Identifying congruence subgroups
of the modular group


Author: Tim Hsu
Journal: Proc. Amer. Math. Soc. 124 (1996), 1351-1359
MSC (1991): Primary 20H05; Secondary 20F05
MathSciNet review: 1343700
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Abstract: We exhibit a simple test (Theorem 2.4) for determining if a given (classical) modular subgroup is a congruence subgroup, and give a detailed description of its implementation (Theorem 3.1). In an appendix, we also describe a more ``invariant'' and arithmetic congruence test.


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Additional Information

Tim Hsu
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Address at time of publication: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: timhsu@math.princeton.edu, timhsu@math.lsa.umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03496-X
PII: S 0002-9939(96)03496-X
Keywords: Congruence subgroups, classical modular group
Received by editor(s): September 1, 1994
Additional Notes: The author was supported by an NSF graduate fellowship and DOE GAANN grant #P200A10022.A03.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1996 American Mathematical Society