89 citations · 1.1k across the 43 of their papers we have counts for
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math.SP2015★ 8 cited
Improved fractal Weyl bounds for hyperbolic manifolds
Semyon Dyatlov, David Borthwick, Tobias Weich
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…
math.AP2015★ 3 cited
Lower resolvent bounds and Lyapunov exponents
Semyon Dyatlov, Alden Waters
We prove a new polynomial lower bound on the scattering resolvent. For that, we construct a quasimode localized on a trajectory which is trapped in the past, but not in the fut…
math.SP2015★ 46 cited
Spectral gaps, additive energy, and a fractal uncertainty principle
Semyon Dyatlov, Joshua Zahl
We obtain an essential spectral gap for -dimensional convex co-compact hyperbolic manifolds with the dimension of the limit set close to . The size of the gap is ex…