Wave 0-trace and length spectrum on convex co-compact hyperbolic manifolds

摘要

For convex co-compact hyperbolic quotients GammaHn+1, we obtain a formula relating the 0-trace of the wave operator with the resonances and some conformal invariants of the boundary, generalizing a formula of Guillope and Zworski in dimension 2. Then, by writing this 0-trace with the length spectrum, we prove precise asymptotics of the number of closed geodesics with an effective, exponentially small error term when the dimension of the limit set of Gamma is greater than n/2.