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math.NT2023
Counting elements of the congruence subgroup
Kamil Bulinski, Igor E. Shparlinski
We obtain asymptotic formulas for the number of matrices in the congruence subgroup \[ Γ_0(Q) = \left\{ A\in\mathrm{SL}_2(\mathbb Z):~c \equiv 0 \pmod Q\right\}, \] which are of na…
math.NT2023★ 1 cited
Counting embeddings of free groups into and its subgroups
Kamil Bulinski, Alina Ostafe, Igor E. Shparlinski
We show that if one selects uniformly independently and identically distributed matrices from a ball of large radius then with…