A Riccati differential equation and free subgroup numbers for lifts of $\PSL_2(\Z)$ modulo powers of primes

Christian Krattenthaler, Thomas W. Müller

It is shown that the number $f_{\lambda }$ of free subgroups of index $6\lambda$ in the modular group $\PSL_2(\Z)$, when considered modulo a prime power $p^\al$ with $p\ge 5$, is always (ultimatel…