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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.02228 |
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Table of Contents:
- Let $Γ$ be a Schottky subgroup of $\mathrm{SL}_2(\mathbb{Z})$ and let $X=Γ\backslash \mathbb{H}^2$ be the associated hyperbolic surface. Conditional on the generalized Riemann hypothesis for quadratic $L$-functions, we establish a uniform and explicit spectral gap for the Laplacian on the Hecke congruence covers $ X_0(p) = Γ_0(p)\backslash \mathbb{H}^2$ of $X$ for "almost" all primes $p$, provided the limit set of $Γ$ is thick enough.