## Abstract

Let G = SL(2, R) n R2 and Γ = SL(2, Z) n Z2. Building on recent work of

Strömbergsson we prove a rate of equidistribution for the orbits of a certain 1-dimensional unipotent flow of Γ\G, which projects to a closed horocycle in the unit tangent bundle to the modular surface. We use this to answer a question of Elkies and McMullen by making effective the convergence of the gap distribution of √

n mod 1.

Strömbergsson we prove a rate of equidistribution for the orbits of a certain 1-dimensional unipotent flow of Γ\G, which projects to a closed horocycle in the unit tangent bundle to the modular surface. We use this to answer a question of Elkies and McMullen by making effective the convergence of the gap distribution of √

n mod 1.

Original language | English |
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Pages (from-to) | 563-584 |

Number of pages | 22 |

Journal | Journal of the London Mathematical Society |

Volume | 83 |

Issue number | 4 |

Early online date | 24 May 2016 |

DOIs | |

Publication status | Published - 1 Oct 2016 |