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Uniform bounds for period integrals and sparse equidistribution

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JournalInternational Mathematics Research Notices
DateE-pub ahead of print - 1 May 2015
DatePublished (current) - 2015
Issue number24
Volume2015
Number of pages23
Pages (from-to)13728-13756
Early online date1/05/15
Original languageEnglish

Abstract

Let $M=\Gamma\backslash\mathrm{PSL}(2,\mathbb{R})$ 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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© The Authors 2015. This is an author produced version of a paper accepted for publication in International Mathematics Research Notices. Uploaded in accordance with the publisher's self-archiving policy.

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  • math.DS, math.NT

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