Journal of Spectral Theory


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Volume 6, Issue 1, 2016, pp. 137–144
DOI: 10.4171/JST/121

Published online: 2016-04-04

A note on the resonance counting function for surfaces with cusps

Yannick Bonthonneau[1]

(1) Université du Québec à Montréal, Canada

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 $O(T^{3/2})$.

Keywords: Resonances, surfaces with cusps, Weyl law

Bonthonneau Yannick: A note on the resonance counting function for surfaces with cusps. J. Spectr. Theory 6 (2016), 137-144. doi: 10.4171/JST/121