Research output: Contribution to journal › Article

**Uniform bounds for period integrals and sparse equidistribution.** / Tanis, James; Vishe, Pankaj.

Research output: Contribution to journal › Article

Tanis, J & Vishe, P 2015, 'Uniform bounds for period integrals and sparse equidistribution', *International Mathematics Research Notices*, vol. 2015, no. 24, pp. 13728-13756. https://doi.org/10.1093/imrn/rnv115

Tanis, J., & Vishe, P. (2015). Uniform bounds for period integrals and sparse equidistribution. *International Mathematics Research Notices*, *2015*(24), 13728-13756. https://doi.org/10.1093/imrn/rnv115

Tanis J, Vishe P. Uniform bounds for period integrals and sparse equidistribution. International Mathematics Research Notices. 2015;2015(24):13728-13756. https://doi.org/10.1093/imrn/rnv115

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title = "Uniform bounds for period integrals and sparse equidistribution",

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 $M$.",

keywords = "math.DS, math.NT",

author = "James Tanis and Pankaj Vishe",

note = "{\circledC} 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.",

year = "2015",

doi = "10.1093/imrn/rnv115",

language = "English",

volume = "2015",

pages = "13728--13756",

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AU - Vishe, Pankaj

N1 - © 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.

PY - 2015

Y1 - 2015

N2 - 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 $M$.

AB - 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 $M$.

KW - math.DS

KW - math.NT

U2 - 10.1093/imrn/rnv115

DO - 10.1093/imrn/rnv115

M3 - Article

VL - 2015

SP - 13728

EP - 13756

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1687-0247

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