On Rademacher's conjecture: congruence subgroups of genus zero of the modular group.
type: Item
instance of: scholarly article
title: On Rademacher's conjecture: congruence subgroups of genus zero of the modular group.
zbMATH Open document ID: 1056.20034
author: Kok Seng Chua
author: Yifan Yang
author: Mong Lung Lang
published in: Journal of Algebra
publication date: 2004-09-23T00:00:00Z
review text: The authors give a complete list of all genus zero congruence subgroups of \(\text{PSL}_2(\mathbb{Z})\). Up to conjugation, there are 132 of them; they also give the geometric invariants associated to each of these subgroups, as well as independent generators for the subgroups, and generators of the associated function field. The finiteness of the list was a conjecture of Rademacher, which was first resolved in the affirmative by J. Dennin, it can also be deduced from J. Thompson's finiteness theorem. Nonetheless, the complete list given here, (which generalizes the list given by Sebbar for the torsion-free genus zero congruence subgroups), as well as the properties of the groups in the list should prove useful for algebraists and number theorists interested in the congruence subgroups of the modular group.
Mathematics Subject Classification ID: 20H05
Mathematics Subject Classification ID: 11F06
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 2102485
zbMATH Keywords: Rademacher conjecture
zbMATH Keywords: congruence subgroups
zbMATH Keywords: modular group
zbMATH Keywords: genera
zbMATH Keywords: numbers of cusps
zbMATH Keywords: indices
zbMATH Keywords: fundamental polygons
zbMATH Keywords: Farey symbols
zbMATH Keywords: generators
zbMATH Keywords: function fields
reviewed by: Ser Peow Tan
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.02.025
OpenAlex ID: W1974379443
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Wikidata QID: Q122981548
DOI: 10.1016/J.JALGEBRA.2004.02.025
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description: scientific article; zbMATH DE number 2102485