Poissonian correlations of higher orders

Manuel Hauke, Agamemnon Zafeiropoulos

Research output: Contribution to journalArticlepeer-review


We show that any sequence (x n) n∈N⊆[0,1] that has Poissonian correlations of k – th order is uniformly distributed, also providing a quantitative description of this phenomenon. Additionally, we extend connections between metric correlations and additive energy, already known for pair correlations, to higher orders. Furthermore, we examine how the property of Poissonian k – th correlations is reflected in the asymptotic size of the moments of the function F(t,s,N)=#{n⩽N:‖x n−t‖⩽s/(2N)},t∈[0,1].

Original languageEnglish
Pages (from-to)202-240
Number of pages39
JournalJournal of Number Theory
Publication statusPublished - Feb 2023


  • Poisson correlations
  • Uniform distribution
  • Poissonian correlations

ASJC Scopus subject areas

  • Algebra and Number Theory


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