English

Counting elements of the congruence subgroup

Number Theory 2024-12-11 v2

Abstract

We obtain asymptotic formulas for the number of matrices in the congruence subgroup Γ0(Q)={ASL2(Z): c0(modQ)}, \Gamma_0(Q) = \left\{ A\in\mathrm{SL}_2(\mathbb Z):~c \equiv 0 \pmod Q\right\}, which are of naive height at most XX. Our result is uniform in a very broad range of values QQ and XX.

Keywords

Cite

@article{arxiv.2308.10485,
  title  = {Counting elements of the congruence subgroup},
  author = {Kamil Bulinski and Igor E. Shparlinski},
  journal= {arXiv preprint arXiv:2308.10485},
  year   = {2024}
}
R2 v1 2026-06-28T12:00:06.442Z