On Rademacher's conjecture: congruence subgroups of genus zero of the modular group.
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.
scientific article; zbMATH DE number 2102485
scientific article