Optimal Farey sequence for the Congruence subgroup ${\Gamma }_0(2^n)$

Nhat Minh Doan, Sang-hyun Kim, Mong Lung Lang +1

We prove that ${\Gamma }_0(2^n)$ ($n\ge 2$) has a Farey sequence $\{e_i\}$ such that $e_i\le 2^{n-1}$ for all $e_i$. The above upper bound is optimal, and there exists a unique $j$ such th…