Density and localization of resonances for convex co-compact hyperbolic surfaces

Let $X$ be a convex co-compact hyperbolic surface and let $\delta$ be the Hausdorff dimension of the limit set of the underlying discrete group. We show that the density of the resonances of the Laplacian in strips ${\sigma\leq \re(s) \leq \delta}$with$|\im(s)| \leq T$islessthan$O(T^{1+\delta-\epsilon(\sigma)})$with$\epsilon>0$aslongas$\sigma>\delta/2$. This improves the fractal Weyl upper bounds of Zworski and supports numerical results obtained for various models of quantum chaotic scattering.