## Uniform bounds for period integrals and sparse equidistribution

Research output: Contribution to journalArticle

### Standard

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

In: International Mathematics Research Notices, Vol. 2015, No. 24, 2015, p. 13728-13756.

Research output: Contribution to journalArticle

### Harvard

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

### APA

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

### Vancouver

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

### Author

Tanis, James ; Vishe, Pankaj. / Uniform bounds for period integrals and sparse equidistribution. In: International Mathematics Research Notices. 2015 ; Vol. 2015, No. 24. pp. 13728-13756.

### Bibtex - Download

@article{58cfbed40d5147fe8247aea2d73bc226,
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",
journal = "International Mathematics Research Notices",
issn = "1687-0247",
publisher = "Oxford University Press",
number = "24",

}

### RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Uniform bounds for period integrals and sparse equidistribution

AU - Tanis, James

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

IS - 24

ER -