On the correlations of nα mod 1

Niclas Technau, Nadav Yesha

Research output: Contribution to journalArticlepeer-review


A well known result in the theory of uniform distribution modulo 1 (which goes back to Fejér and Csillag) states that the fractional parts 1nαºof 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 (1nαº)n≥1 are of fundamental importance. We prove that for each k ≥ 2; the k-level correlation function Rk is Poissonian for almost every α > 4k2 - 4k - 1.

Original languageEnglish
Pages (from-to)4123-4154
Number of pages32
JournalJournal of the European Mathematical Society
Issue number10
StatePublished - 2023

Bibliographical note

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


  • Uniform distribution modulo 1
  • correlation functions
  • local statistics

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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