A note on the resonance counting function for surfaces with cusps

Yannick Bonthonneau (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

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

Domaines: Théorie spectrale [math.SP]

Yannick Bonthonneau. A note on the resonance counting function for surfaces with cusps. 2014. ⟨hal-00994336⟩