## Abstract

A well known result in the theory of uniform distribution modulo 1 (which goes back to Fejér and Csillag) states that the fractional parts ^{1}nαºof the sequence (nα)_{n≥1} are uniformly distributed in the unit interval whenever α > 0 is not an integer. For sharpening this knowledge to local statistics, the k-level correlation functions of the sequence (^{1}nαº)_{n≥1} are of fundamental importance. We prove that for each k ≥ 2; the k-level correlation function R_{k} is Poissonian for almost every α > 4k^{2} - 4k - 1.

Original language | English |
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Pages (from-to) | 4123-4154 |

Number of pages | 32 |

Journal | Journal of the European Mathematical Society |

Volume | 25 |

Issue number | 10 |

DOIs | |

State | Published - 2023 |

### Bibliographical note

Publisher Copyright:© 2022 European Mathematical Society Published by EMS Press and licensed under a CC BY 4.0 license.

## Keywords

- Uniform distribution modulo 1
- correlation functions
- local statistics

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics

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