An Effective Slope Gap Distribution for Lattice Surfaces
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917784409079808 |
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| author | Osman, Tariq Southerland, Joshua Wang, Jane |
| author_facet | Osman, Tariq Southerland, Joshua Wang, Jane |
| contents | We prove an effective slope gap distribution result first for the square torus and then for general lattice translation surfaces. As a corollary, we obtain a dynamical proof for an effective gap distribution result for the Farey fractions. As an intermediate step, we prove an effective equidistribution result for the intersection points of long horocycles with a particular transversal of the horocycle flow in $\mathrm{SL}_2 (\mathbb R)/Γ$ where $Γ$ is a lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Effective Slope Gap Distribution for Lattice Surfaces Osman, Tariq Southerland, Joshua Wang, Jane Dynamical Systems Geometric Topology Number Theory 37A17, 37D40, 32G15 We prove an effective slope gap distribution result first for the square torus and then for general lattice translation surfaces. As a corollary, we obtain a dynamical proof for an effective gap distribution result for the Farey fractions. As an intermediate step, we prove an effective equidistribution result for the intersection points of long horocycles with a particular transversal of the horocycle flow in $\mathrm{SL}_2 (\mathbb R)/Γ$ where $Γ$ is a lattice. |
| title | An Effective Slope Gap Distribution for Lattice Surfaces |
| topic | Dynamical Systems Geometric Topology Number Theory 37A17, 37D40, 32G15 |
| url | https://arxiv.org/abs/2409.15660 |