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Journal | International Mathematics Research Notices |
---|---|

Date | E-pub ahead of print - 1 May 2015 |

Date | Published (current) - 2015 |

Issue number | 24 |

Volume | 2015 |

Number of pages | 23 |

Pages (from-to) | 13728-13756 |

Early online date | 1/05/15 |

Original language | English |

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 $M$.

© 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.

- math.DS, math.NT

## Programme Grant-New Frameworks in metric Number Theory

Project: Research project (funded) › Research

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