Abstract
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 language | English |
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Pages (from-to) | 202-240 |
Number of pages | 39 |
Journal | Journal of Number Theory |
Volume | 243 |
DOIs | |
Publication status | Published - Feb 2023 |
Keywords
- Poisson correlations
- Uniform distribution
- Poissonian correlations
ASJC Scopus subject areas
- Algebra and Number Theory