The authors provide a proof of the optimal polynomial lower bound for the number of resonances of a surface with hyperbolic ends. They also give Weyl asymptotics for relative scattering phase of such a surface. The authors remark that the main technical ingredient in their paper is a new proof of the Poisson formula, which also applies in the Euclidean model, and that from the point of view of scattering theory – finite volume quotients have one-dimensional infinity [one may see: J. Sjöstrand and M. Zworski, Commun. Partial Differ. Equations 17, No. 5/6, 1021-1035 (1992; Zbl 0766.35031)].
The methods used in the paper (except for the general aspects of the proof of the Poisson formula) are related to L. Guillopé and M. Zworski [J. Funct. Anal. 129, No. 2, 364-389 (1995; Zbl 0841.58063)].