Explicit spectral gap for Schottky subgroups of $\mathrm{SL} (2,\mathbb{Z})$

Irving Calderón; Michael Magee

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arXiv · 2303.17950

Explicit spectral gap for Schottky subgroups of $\mathrm{SL} (2,\mathbb{Z})$

Irving Calderón·Michael Magee

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Abstract

Let $\Gamma$ be a Schottky subgroup of $\mathrm{SL} (2,\mathbb{Z})$. We establish a uniform and explicit lower bound of the second eigenvalue of the Laplace-Beltrami operator of congruence coverings of the hyperbolic surface $\Gamma \backslash \mathbb{H}^2$ provided the limit set of $\Gamma$ is thick enough.

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Irving Calderón, Michael Magee. 2023-03-31. Explicit spectral gap for Schottky subgroups of $\mathrm{SL} (2,\mathbb{Z})$. https://arxiv.org/abs/2303.17950

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