On a multi-dimensional Poissonian pair correlation concept and uniform distribution

DOI10.1007/s00605-019-01267-9zbMath1443.11149arXiv1809.05672OpenAlexW2963214620WikidataQ128324692 ScholiaQ128324692MaRDI QIDQ2274064

Aicke Hinrichs, Lisa Kaltenböck, Wolfgang Stockinger, Mario Ullrich, Gerhard Larcher

Publication date: 19 September 2019

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.05672

zbMATH Keywords

uniform distributionadditive energypair correlation of sequences

Mathematics Subject Classification ID

General theory of distribution modulo (1) (11K06) Special sequences (11K31) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (11)

Pair correlations of Halton and Niederreiter sequences are not Poissonian ⋮ Remarks about inhomogeneous pair correlations ⋮ On higher dimensional Poissonian pair correlation ⋮ Deviation from equidistance for one-dimensional sequences ⋮ The pair correlation function of multi-dimensional low-discrepancy sequences with small stochastic error terms ⋮ On the number of gaps of sequences with Poissonian pair correlations ⋮ Poissonian pair correlation in higher dimensions ⋮ A note on sequences not having metric Poissonian pair correlations ⋮ Pair correlation and equidistribution on manifolds ⋮ Some connections between discrepancy, finite gap properties, and pair correlations ⋮ Poissonian correlations of higher orders

Cites Work

• Unnamed Item
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• Pair correlations of sequences in higher dimensions
• The pair correlation function of fractional parts of polynomials
• Additive energy and the Hausdorff dimension of the exceptional set in metric pair correlation problems
• Some negative results related to Poissonian pair correlation problems
• GCD sums and sum-product estimates
• Pair correlations and equidistribution
• On pair correlation and discrepancy
• Pair correlation for fractional parts of αn²
• A metric result on the pair correlation of fractional parts of sequences
• THE PRIMES ARE NOT METRIC POISSONIAN
• On Quasi-Energy-Spectra, Pair Correlations of Sequences and Additive Combinatorics
• GCD sums and complete sets of square-free numbers
• THERE IS NO KHINTCHINE THRESHOLD FOR METRIC PAIR CORRELATIONS
• The Distribution of Directions in an Affine Lattice: Two-Point Correlations and Mixed Moments
• The two-point correlation function of the fractional parts of $\sqrt {n}$ is Poisson
• Localized quantitative criteria for equidistribution
• DISTRIBUTION MODULO ONE AND RATNER’S THEOREM
• The distribution of spacings between the fractional parts of \(n^2\alpha\)

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