JournalsjstVol. 6, No. 1pp. 137–144

A note on the resonance counting function for surfaces with cusps

  • Yannick Guedes Bonthonneau

    Université du Québec à Montréal, Canada
A note on the resonance counting function for surfaces with cusps cover
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Abstract

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 TT \to \infty with remainder O(T3/2)O(T^{3/2}).

Cite this article

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

DOI 10.4171/JST/121