Improved fractal Weyl bounds for hyperbolic manifolds (with an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich)

  • Semyon Dyatlov

    Massachusetts Institute of Technology, Cambridge, USA
Improved fractal Weyl bounds for hyperbolic manifolds (with an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich) cover

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Abstract

We give a new fractal Weyl upper bound for resonances of convex co-compact hyperbolic manifolds in terms of the dimension of the manifold and the dimension of its limit set. More precisely, we show that as , the number of resonances in the box is , where the exponent changes its behavior at . In the case , we also give an improved resolvent upper bound in the standard resonance free strip . Both results use the fractal uncertainty principle point of view recently introduced in [DyZa]. The appendix presents numerical evidence for the Weyl upper bound.

Cite this article

Semyon Dyatlov, Improved fractal Weyl bounds for hyperbolic manifolds (with an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich). J. Eur. Math. Soc. 21 (2019), no. 6, pp. 1595–1639

DOI 10.4171/JEMS/867