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arXiv · 1501.05228

Uniform bounds for period integrals and sparse equidistribution

James Tanis·Pankaj Vishe
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Abstract

Let $M=Γ\backslash\mathrm{PSL}(2,\mathbb{R})$ be a compact manifold, and let $f\in C^\infty(M)$ be a function of zero average. We use spectral methods to get uniform (i.e. independent of spectral gap) bounds for twisted averages of $f$ along long horocycle orbit segments. We apply this to obtain an equidistribution result for sparse subsets of horocycles on $M$.

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James Tanis, Pankaj Vishe. 2015-01-21. Uniform bounds for period integrals and sparse equidistribution. https://arxiv.org/abs/1501.05228

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