Some negative results related to Poissonian pair correlation problems

DOI10.1016/j.disc.2019.111656zbMath1436.11091arXiv1803.05236OpenAlexW2979950107WikidataQ127108047 ScholiaQ127108047MaRDI QIDQ2279979

Gerhard Larcher, Wolfgang Stockinger

Publication date: 17 December 2019

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.05236

zbMATH Keywords

normal numbersspecial sequencesPoissonian pair correlations

Mathematics Subject Classification ID

General theory of distribution modulo (1) (11K06)

Related Items (19)

Multi-dimensional Kronecker sequences with a small number of gap lengths ⋮ Pair correlations of Halton and Niederreiter sequences are not Poissonian ⋮ Remarks about inhomogeneous pair correlations ⋮ On exceptional sets in the metric Poissonian pair correlations problem ⋮ The champernowne constant is not Poissonian ⋮ Deviation from equidistance for one-dimensional sequences ⋮ The pair correlation function of multi-dimensional low-discrepancy sequences with small stochastic error terms ⋮ Pair correlations of logarithms of complex lattice points ⋮ The metric theory of the pair correlation function of real-valued lacunary sequences ⋮ On the number of gaps of sequences with Poissonian pair correlations ⋮ Poissonian pair correlation in higher dimensions ⋮ On a multi-dimensional Poissonian pair correlation concept and uniform distribution ⋮ On the pair correlations of powers of real numbers ⋮ Pair correlation and equidistribution on manifolds ⋮ Pair correlation of sequences with maximal additive energy ⋮ Low discrepancy sequences failing Poissonian pair correlations ⋮ Some connections between discrepancy, finite gap properties, and pair correlations ⋮ On the statistics of pairs of logarithms of integers ⋮ Sequences with almost Poissonian pair correlations

Cites Work

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• Point sets and sequences with small discrepancy
• A generalization of Kakutani's splitting procedure
• 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
• Discrepancy of \(LS\)-sequences of partitions and points
• On extending de Bruijn sequences
• Pair correlations and equidistribution
• On pair correlation and discrepancy
• On exceptional sets in the metric Poissonian pair correlations problem
• The champernowne constant is not Poissonian
• Pair correlation for fractional parts of αn²
• A metric result on the pair correlation of fractional parts of sequences
• On the uniform ε-distribution of residues within the periods of rational fractions with applications to normal numbers
• ADDITIVE ENERGY AND THE METRIC POISSONIAN PROPERTY
• On Quasi-Energy-Spectra, Pair Correlations of Sequences and Additive Combinatorics
• 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
• A strong hot spot theorem
• An alternative construction of normal numbers
• The distribution of spacings between the fractional parts of \(n^2\alpha\)

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