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| Format: | Preprint |
| Publié: |
2023
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| Accès en ligne: | https://arxiv.org/abs/2305.02228 |
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| _version_ | 1866918459748646912 |
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| author | Soares, Louis |
| author_facet | Soares, Louis |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02228 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Explicit spectral gap for Hecke congruence covers of arithmetic Schottky surfaces Soares, Louis Spectral Theory Differential Geometry Number Theory 58J50 (Primary) 11M36, 11F06 (Secondary) 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. |
| title | Explicit spectral gap for Hecke congruence covers of arithmetic Schottky surfaces |
| topic | Spectral Theory Differential Geometry Number Theory 58J50 (Primary) 11M36, 11F06 (Secondary) |
| url | https://arxiv.org/abs/2305.02228 |