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arXiv · 2308.10485

Counting elements of the congruence subgroup

Kamil Bulinski·Igor E. Shparlinski
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Abstract

We obtain asymptotic formulas for the number of matrices in the congruence subgroup \[ \Gamma_0(Q) = \left\{ A\in\mathrm{SL}_2(\mathbb Z):~c \equiv 0 \pmod Q\right\}, \] which are of naive height at most $X$. Our result is uniform in a very broad range of values $Q$ and $X$.

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Kamil Bulinski, Igor E. Shparlinski. 2023-08-21. Counting elements of the congruence subgroup. https://doi.org/10.4153/s0008439524000365

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