Strong spectral gaps for compact quotients of products of )
The existence of a strong spectral gap for quotients of noncompact connected semisimple Lie groups is crucial in many applications. For congruence lattices there are uniform and very good bounds for the spectral gap coming from the known bounds towards the Ramanujan–Selberg conjectures. If has no compact factors then for general lattices a spectral gap can still be established, but there is no uniformity and no effective bounds are known. This note is concerned with the spectral gap for an irreducible...