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 with remainder .
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Yannick Guedes Bonthonneau, A note on the resonance counting function for surfaces with cusps. J. Spectr. Theory 6 (2016), no. 1, pp. 137–144DOI 10.4171/JST/121