A uniform spectral gap for congruence covers of a hyperbolic manifold

Dubi Kelmer, Lior Silberman

Let $G$ be $\SO(n,1)$ or $\SU(n,1)$ and let $\Gamma \subset G$ denote an arithmetic lattice. The hyperbolic manifold $Γ\backslash \calH$ comes with a natural family of covers, coming fro…