A note on the resonance counting function for surfaces with cusps (Q294066)

Summary: We prove sharp upper bounds for the number of resonances in boxes of size 1 at high frequency for the Laplacian on finite volume surfaces with hyperbolic cusps. As a corollary, we obtain a Weyl asymptotic for the number of resonances in balls of size \(T \to \infty\) with remainder \(O(T^{3/2})\).