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arXiv · 2409.15660

An Effective Slope Gap Distribution for Lattice Surfaces

Tariq Osman·Joshua Southerland·Jane Wang
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Abstract

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 $\mathrm{SL}_2 (\mathbb R)/\Gamma$ where $\Gamma$ is a lattice.

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Tariq Osman, Joshua Southerland, Jane Wang. 2024-09-24. An Effective Slope Gap Distribution for Lattice Surfaces. https://arxiv.org/abs/2409.15660

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