Counting congruence subroups
| dc.creator | Goldfeld, D. | |
| dc.creator | Lubotzky, A. | |
| dc.creator | Pyber, L. | |
| dc.date | 2004-06-12 | |
| dc.date.accessioned | 2026-07-07T05:09:11Z | |
| dc.date.available | 2026-07-07T05:09:11Z | |
| dc.description | Let $Γ$ denote the modular group $SL(2,\Bbb Z)$ and $C_n(Γ)$ the number of congruence subgroups of $Γ$ of index at most $n$. We prove that $\lim\limits_{n\to \infty} \frac{\log C_n(Γ)}{(\log n)^2/\log\log n} = \frac{3-2\sqrt{2}}{4}.$ We also present a very general conjecture giving an asymptotic estimate for $C_n(Γ)$ for general arithmetic groups. The lower bound of the conjecture is proved modulo the generalized Riemann hypothesis for Artin-Hecke L-functions, and in many cases is also proved unconditionally. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/math/0406249 | |
| dc.identifier | http://arxiv.org/abs/math/0406249 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71539 | |
| dc.subject | Group Theory | |
| dc.title | Counting congruence subroups | |
| dc.type | text |