# Strong Spectral Gaps for Compact Quotients of Products of \$PSL2,bR\$ - Mathematics > Number Theory

Strong Spectral Gaps for Compact Quotients of Products of \$PSL2,bR\$ - Mathematics > Number Theory - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: The existence of a strong spectral gap for quotients \$\Gamma\bs G\$ ofnoncompact connected semisimple Lie groups is crucial in many applications. Forcongruence lattices there are uniform and very good bounds for the spectral gapcoming from the known bounds towards the Ramanujan-Selberg Conjectures. If \$G\$has no compact factors then for general lattices a strong spectral gap canstill be established, however, there is no uniformity and no effective boundsare known. This note is concerned with the strong spectral gap for anirreducible co-compact lattice \$\Gamma\$ in \$G=\PSL2,\bbR^d\$ for \$d\geq 2\$which is the simplest and most basic case where the congruence subgroupproperty is not known. The method used here gives effective bounds for thespectral gap in this setting.

Autor: Dubi Kelmer, Peter Sarnak

Fuente: https://arxiv.org/