Louis Soares

activity

20172026

most citedLarge covers and sharp resonances of hyperbolic surfaces

6 citations · 6 across the 6 of their papers we have counts for

collaborators

10 papers

math.SP2026

Resonance counting and spectral gaps for hyperbolic surfaces via Fourier decay

Louis Soares

We prove an improved fractal Weyl upper bound for resonances of infinite-area convex cocompact hyperbolic surfaces, expressed in terms of the Hausdorff dimension of the limit set a…

math.SP2023

Explicit spectral gap for Hecke congruence covers of arithmetic Schottky surfaces

Louis Soares

Let $Γ$ be a Schottky subgroup of $SL_{2} (Z)$ and let $X = Γ\ H^{2}$ be the associated hyperbolic surface. Conditional on the generalized Riemann hypo…

math.SP2023

Low-lying resonances for infinite-area hyperbolic surfaces with long closed geodesics

Louis Soares

We consider sequences $(X_{n})_{n \in N}$ of coverings of convex cocompact hyperbolic surfaces $X$ with Euler characterictic $χ (X_{n})$ tending to $- \infty$ as $n \to \infty.$ W…

math.SP2023

Improved fractal Weyl bounds for convex cocompact hyperbolic surfaces and large resonance-free regions

Louis Soares

Let $X$ be a convex cocompact hyperbolic surface, and let $δ$ denote the Hausdorff dimension of its limit set. Let $N_{X} (σ, T)$ denote the number of resonances of $X$ inside the box…

math.SP2021

Uniform resonance free regions for convex cocompact hyperbolic surfaces and expanders

Louis Soares

We prove that every family of coverings of any infinite-area, convex cocompact hyperbolic surface has uniform spectral gap, provided that the associated Schreier graphs form a fami…

math.SP2020

Hecke triangle groups, transfer operators and Hausdorff dimension

Louis Soares

We consider the family of Hecke triangle groups $Γ_{w} = ⟨ S, T_{w} ⟩$ generated by the Möbius transformations $S : z \mapsto - 1/ z$ and $T_{w} : z \mapsto z + w$ with $…

math.SP2018

Fractal Weyl bounds and Hecke triangle groups

Frederic Naud, Anke Pohl, Louis Soares

Let $Γ_{w}$ be a non-cofinite Hecke triangle group with cusp width $w > 2$ and let $ϱ : Γ_{w} \to U (V)$ be a finite-dimensional unitary representation of $Γ_{w}$ . In this note we…

math.SP2018

Density of Resonances for Covers of Schottky Surfaces

Anke Pohl, Louis Soares

We investigate how bounds of resonance counting functions for Schottky surfaces behave under transitions to covering surfaces of finite degree. We consider the classical resonance…

math.SP2017★ 6 cited

Large covers and sharp resonances of hyperbolic surfaces

Dmitry Jakobson, Frederic Naud, Louis Soares

Let $Γ$ be a convex co-compact discrete group of isometries of the hyperbolic plane $H^{2}$ , and $X = Γ\ H^{2}$ the associated surface. In this paper we invest…

math.SP2017

Hyperbolic Surfaces with Arbitrarily Small Spectral Gap

Louis Soares

Let $X = Γ ∖ H$ be a non-elementary geometrically finite hyperbolic surface and let $δ$ denote the Hausdorff dimension of the limit set $Λ (Γ)$ . We prove that f…