On the resonances of convex co-compact subgroups of arithmetic groups

Abstract

Let $\Lambda$ be a non-elementary convex co-compact fuchsian group which is a subgroup of an arithmetic fuchsian group. We prove that the Laplace operator of the hyperbolic surface $X=Λ\backslash\H$ has infinitely many resonances in an effective strip depending on the dimension of the limit set $\delta$. Applications to lower bounds for the hyperbolic lattice point counting problem are derived.

18 pages

References in corpus (1)

• Wave decay on convex co-compact hyperbolic manifolds

Cited by in corpus (1)

• Resonances in open quantum maps