UPPER-BOUNDS ON THE NUMBER OF RESONANCES FOR NONCOMPACT RIEMANN SURFACES

Let X be a Riemannian surface of finite geometric type and with hyperbolic ends. The resolvent (Delta(X)-s(l-s))(-1), Res > l of the Laplacian on X extends to a meromorphic family of operators on C and its poles are called resonances. We prove an optimal polynomial bound for their counting function. (C) 1995 Academic Press, Inc.