Uniform congruence counting for Schottky semigroups in ${\mathrm{SL}}_2(\mathbf{Z})$

Michael Magee, Hee Oh, Dale Winter

Let $\Gamma$ be a Schottky semigroup in ${\mathrm{SL}}_2(\mathbf{Z})$, and for $q\in \mathbf{N}$, let $Γ(q):=\{γ\in Γ: γ= e \text{ (mod $q$)}\}$ be its congruence subsemigroup of level $q$…