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 $|\im(s)| \leq T$ is less than $O(T^{1+\delta-\epsilon(\sigma)})$ with $\epsilon>0$ as long as $\sigma>\delta/2$. This improves the fractal Weyl upper bounds of Zworski and supports numerical results obtained for various models of quantum chaotic scattering. 
Fr\'ed\'eric Naud (LANLG)
math.SP