Poissonian pair correlation in higher dimensions

DOI10.1016/j.jnt.2019.07.011zbMath1445.11077arXiv1812.10458OpenAlexW2970204516MaRDI QIDQ2009148

Stefan Steinerberger

Publication date: 27 November 2019

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.10458

zbMATH Keywords

pair correlationuniform distributionexponential sims

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Positive definite functions in one variable harmonic analysis (42A82) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Miscellaneous topics in measure theory (28E99) General theory of distribution modulo (1) (11K06)

Related Items (9)

Pair correlations of Halton and Niederreiter sequences are not Poissonian ⋮ On higher dimensional Poissonian pair correlation ⋮ The pair correlation function of multi-dimensional low-discrepancy sequences with small stochastic error terms ⋮ Poissonian correlation of higher order differences ⋮ On the number of gaps of sequences with Poissonian pair correlations ⋮ Pair correlation and equidistribution on manifolds ⋮ Some connections between discrepancy, finite gap properties, and pair correlations ⋮ Poissonian correlations of higher orders ⋮ Sequences with almost Poissonian pair correlations

Cites Work

• Unnamed Item
• Pair correlations of sequences in higher dimensions
• The pair correlation function of fractional parts of polynomials
• Pair correlation densities of inhomogeneous quadratic forms
• Poissonian pair correlation and discrepancy
• Pair correlation of values of rational functions (mod \(p\))
• Small values of \(n^ 2\alpha\pmod 1\)
• On a multi-dimensional Poissonian pair correlation concept and uniform distribution
• Some negative results related to Poissonian pair correlation problems
• Pair correlations and equidistribution
• On pair correlation and discrepancy
• General and refined Montgomery lemmata
• The distribution of spacings between fractional parts of lacunary sequences
• Pair correlation for fractional parts of αn²
• Minimal theta functions
• A metric result on the pair correlation of fractional parts of sequences
• THE PRIMES ARE NOT METRIC POISSONIAN
• 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
• ON THE DISTRIBUTION OF THE SEQUENCE n2  (mod 1)
• The distribution of spacings between the fractional parts of \(n^2\alpha\)

This page was built for publication: Poissonian pair correlation in higher dimensions