# Tagged Questions

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### A question about Ahlfors's proof of modular function being a covering space of the twice punctured plane

I have a question about Ahlfors's proof of modular function being a covering space of the twice punctured plane .See Ahlfors' complex analysis, second edition, page 272. You can either explain or ...

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### Automorphisms of a matrix in Smith normal form?

Added: Amritanshu Prasad's answer makes it clear that I am really asking for a description of the group of integer unimodular matrices $P$ such that $D^{-1}PD$ is also integer. These matrices are ...

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### Congruence subgroups as abstract groups

This is probably well know, and maybe even trivial, but not to me. Consider for concreteness the subgroup
$$
\pm\Gamma_0(3)=\left\{\begin{pmatrix}a & b \\ c & ...

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### Congruence Subgroups as Open Subgroups of the Modular Group Under the Right Topology

It occurred to me that a subgroup of the modular group $\Gamma$ is a congruence subgroup iff it contains a subgroup of the form $\Gamma(N)$, while a subgroup of a general topological group is open iff ...

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### Distinguishing congruence subgroups of the modular group

This question is something of a follow-up to
Transformation formulae for classical theta functions .
How does one recognise whether a subgroup of the modular group
$\Gamma=\mathrm{SL}_2(\mathbb{Z})$ ...