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For all convex co-compact hyperbolic surfaces, we prove the existence of an essential
spectral gap, that is, a strip beyond the unitarity axis in which the Selberg zeta function has …

We obtain an essential spectral gap for n-dimensional convex co-compact hyperbolic
manifolds with the dimension δ δ of the limit set close to n-1\over 2 n-1 2. The size of the gap …

Let G be a connected semisimple real algebraic group, and Γ< G a Zariski dense Anosov
subgroup with respect to a minimal parabolic subgroup. We describe the asymptotic …

We obtain an essential spectral gap for a convex co-compact hyperbolic surface M= Γ
\\mathbb H^ 2 M= Γ\H 2 which depends only on the dimension δ δ of the limit set. More …

We obtain an analog of the prime number theorem for a class of branched covering maps on
the 2-sphere S 2 called expanding Thurston maps, which are topological models of some …

We obtain an analog of the prime number theorem for a class of branched covering maps on
the 2-sphere S 2 called expanding Thurston maps, which are topological models of some …

We prove a fractal uncertainty principle with exponent $\frac {d}{2}-\delta+\varepsilon $,
$\varepsilon> 0$, for Ahlfors--David regular subsets of $\mathbb R^ d $ with dimension …

In the second paper [16] of this series, we obtained an analog of the prime number theorem
for a class of branched covering maps on the 2-sphere S 2 called expanding Thurston maps …

We introduce a permutation model for random degree nn covers X n X_n of a non-
elementary convex-cocompact hyperbolic surface X= Γ∖ HX=Γ\H. Let δ δ be the Hausdorff …