Geodesic
Counting elements of the congruence subgroup
Canadian mathematical bulletin, Tome 67 (2024) no. 4, pp. 955-969

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DOI

We obtain asymptotic formulas for the number of matrices in the congruence subgroup $$\begin{align*}\Gamma_0(Q) = \left\{ A\in\operatorname{SL}_2({\mathbb Z}):~c \equiv 0 \quad\pmod Q\right\}, \end{align*}$$which are of naive height at most X. Our result is uniform in a very broad range of values Q and X.
DOI : 10.4153/S0008439524000365
Mots-clés : SL2(Z) matrices, congruence subgroup, modular hyperbola 
Bulinski, Kamil; Shparlinski, Igor E. Counting elements of the congruence subgroup. Canadian mathematical bulletin, Tome 67 (2024) no. 4, pp. 955-969. doi: 10.4153/S0008439524000365
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     title = {Counting elements of the congruence subgroup},
     journal = {Canadian mathematical bulletin},
     pages = {955--969},
     year = {2024},
     volume = {67},
     number = {4},
     doi = {10.4153/S0008439524000365},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000365/}
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