Poissonian correlations of higher orders

Manuel Hauke, Agamemnon Zafeiropoulos

Publikation: Beitrag in einer FachzeitschriftArtikelBegutachtung


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].

Seiten (von - bis)202-240
FachzeitschriftJournal of Number Theory
PublikationsstatusVeröffentlicht - Feb. 2023

ASJC Scopus subject areas

  • Algebra und Zahlentheorie


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