Abstract
. We prove that cocompact arithmetic lattices in a simple Lie group are uniformly discrete if and only if Salem numbers are uniformly bounded away from 1. We also prove an analogous result for semisimple Lie groups. Finally, we shed some light on the structure of the bottom of the length spectrum of an arithmetic orbifold Gamma\X by showing the existence of a positive constant delta(X) > 0 such that squares of lengths of closed geodesics shorter than delta must be pairwise linearly dependent over Q.