A quantitative study of orbit counting and discrete spectrum for anti-de Sitter 3-manifolds

Abstract

: Let (cid:2) be a discontinuous group for the 3-dimensional anti-de Sitter space AdS 3 : ¼ SO 0 ð 2 ; 2 Þ = SO 0 ð 2 ; 1 Þ . In this article, we discuss a growth rate of the counting of (cid:2) -orbits at infinity and the discrete spectrum of the hyperbolic Laplacian of the complete anti-de Sitter manifold (cid:2) n AdS 3 .