Louis Soares

activity

20172020

most citedLarge covers and sharp resonances of hyperbolic surfaces

6 citations · 6 across the 2 of their papers we have counts for

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5 papers · 1 filter

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…