### Abstract

We formulate and prove a finite version of Vinogradov's bilinear sum inequality. We use it together with Ratner's joinings theorems to prove that the Moebius function is disjoint from discrete horocycle flows on Γ\SL_{2}(ℝ), where Γ ⊂ SL_{2}(ℝ) is a lattice.

Original language | English (US) |
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Title of host publication | From Fourier Analysis and Number Theory to Radon Transforms and Geometry |

Subtitle of host publication | In Memory of Leon Ehrenpreis |

Editors | Hershel Farkas, Marvin Knopp, Robert Gunning, B.A Taylor |

Pages | 67-83 |

Number of pages | 17 |

DOIs | |

State | Published - Sep 2 2013 |

### Publication series

Name | Developments in Mathematics |
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Volume | 28 |

ISSN (Print) | 1389-2177 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Keywords

- Disjointness of dynamical systems
- Entropy
- Moebius function
- Randomness principle
- Square-free flow
- Vinogradov's bilinear sums

## Fingerprint Dive into the research topics of 'Disjointness of moebius from horocycle flows'. Together they form a unique fingerprint.

## Cite this

Bourgain, J., Sarnak, P., & Ziegler, T. (2013). Disjointness of moebius from horocycle flows. In H. Farkas, M. Knopp, R. Gunning, & B. A. Taylor (Eds.),

*From Fourier Analysis and Number Theory to Radon Transforms and Geometry: In Memory of Leon Ehrenpreis*(pp. 67-83). (Developments in Mathematics; Vol. 28). https://doi.org/10.1007/978-1-4614-4075-8_5