## Uniform bounds for period integrals and sparse equidistribution

Research output: Contribution to journalArticle

## Department/unit(s)

### Publication details

Journal International Mathematics Research Notices E-pub ahead of print - 1 May 2015 Published (current) - 2015 24 2015 23 13728-13756 1/05/15 English

### 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 $M$.

### Bibliographical note

© 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.

### Research areas

• math.DS, math.NT

• ## Programme Grant-New Frameworks in metric Number Theory

Project: Research project (funded)Research

## Discover related content

Find related publications, people, projects, datasets and more using interactive charts.