Matrix coefficients, counting and primes for orbits of geometrically finite groups
Matrix coefficients, counting and primes for orbits of geometrically finite groups
Let G:=\mathrm {SO}(n,1)^\circ and \Gamma<G be a geometrically finite Zariski dense subgroup with critical exponent \delta bigger than (n-1)/2 . Under a spectral gap hypothesis on L^2(\Gamma \backslash G) , which is always satisfied when \delta>(n-1)/2 for n=2,3 and when \delta>n-2 for n\geq 4 , we obtain an effective archimedean …