Poissonian correlations of higher orders

DOI10.1016/J.JNT.2022.08.007arXiv2107.06523MaRDI QIDQ6372755

Manuel Hauke, Agamemnon Zafeiropoulos

Publication date: 14 July 2021

Abstract: We show that any sequence $(x_n{)}_{ninmathbbN}subseteq[0,1]$ 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 $$

Mathematics Subject Classification ID

Probabilistic theory: distribution modulo (1); metric theory of algorithms (11K99) Distribution modulo one (11J71) General theory of distribution modulo (1) (11K06)

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