33 citations · 102 across the 19 of their papers we have counts for
14 papers · 1 filter
Determinants of Laplacians on random hyperbolic surfaces
Frédéric Naud
We investigate the behaviour of the regularized determinant of the Laplace-Beltrami operator on compact hyperbolic surfaces when the genus goes to infinity. We show that for all po…
On the spectrum of twisted Laplacians and the Teichmüller representation
Frédéric Naud, Polyxeni Spilioti
We consider Laplacians with non unitary twists acting on sections of flat vector bundles over compact hyperbolic surfaces. These non self-adjoint Laplacians have discrete spectrum…
Extension of Alon's and Friedman's conjectures to Schottky surfaces
Michael Magee, Frédéric Naud
Let be a Schottky surface, that is, a conformally compact hyperbolic surface of infinite area. Let denote the Hausdorff dimension of the limit set of…
A random cover of a compact hyperbolic surface has relative spectral gap
Michael Magee, Frédéric Naud, Doron Puder
Let be a compact connected hyperbolic surface, that is, a closed connected orientable smooth surface with a Riemannian metric of constant curvature -1. For each $n\in\mathbf{N}…
Explicit spectral gaps for random covers of Riemann surfaces
Michael Magee, Frédéric Naud
We introduce a permutation model for random degree covers of a non-elementary convex-cocompact hyperbolic surface . Let be the Hausdorff di…
Fractal Weyl bounds and Hecke triangle groups
Frederic Naud, Anke Pohl, Louis Soares
Let be a non-cofinite Hecke triangle group with cusp width and let be a finite-dimensional unitary representation of . In this note we…
Spectral gaps and abelian covers of convex co-compact surfaces
Frederic Naud
Given a convex co-compact hyperbolic surface , we investigate the resonance spectrum of the laplacian on large finite abelian cove…
Large covers and sharp resonances of hyperbolic surfaces
Dmitry Jakobson, Frederic Naud, Louis Soares
Let be a convex co-compact discrete group of isometries of the hyperbolic plane , and the associated surface. In this paper we invest…
L-functions and sharp resonances of infinite index congruence subgroups of
Dmitry Jakobson, Frederic Naud
For convex co-compact subgroups of SL2(Z) we consider the "congruence subgroups" for p prime. We prove a factorization formula for the Selberg zeta function in term of L-functions…
On the nodal lines of Eisenstein series on Schottky surfaces
Jakobson Dmitry, Naud Frederic
On convex co-compact hyperbolic surfaces with Hausdorff dimension of the limit set less than 1/2, we investigate high energy behaviour of Eisenstein Series. Eisenstein Series are n…
Resonances and convex co-compact congruence subgroups of PSL2(Z)
Frédéric Naud, Dmitry Jakobson
This papers deals with congruence subgroups of convex cocompact subgroups of PSL2(Z). We examine the behaviour of the resonance spectrum when the congruence parameter q goes to inf…
Density and localization of resonances for convex co-compact hyperbolic surfaces
Frédéric Naud
Let be a convex co-compact hyperbolic surface and let be the Hausdorff dimension of the limit set of the underlying discrete group. We show that the density of the resonanc…
Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds
Colin Guillarmou, Frederic Naud
For convex co-compact hyperbolic manifolds for which the dimension of the limit set satisfies , we show that the high-frequency Eisenstein…
On the resonances of convex co-compact subgroups of arithmetic groups
Dmitry Jakobson, Frédéric Naud
Let be a non-elementary convex co-compact fuchsian group which is a subgroup of an arithmetic fuchsian group. We prove that the Laplace operator of the hyperbolic surface $X=Λ\…