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Counting elements of the congruence subgroup

Published 21 Aug 2023 in math.NT | (2308.10485v2)

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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