ADDITIVE ENERGY AND THE METRIC POISSONIAN PROPERTY

DOI10.1112/S0025579318000207zbMath1441.11185arXiv1709.02634MaRDI QIDQ4555389

Thomas F. Bloom, Aled Walker, Ayla Gafni, Sam Chow

Publication date: 20 November 2018

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.02634

zbMATH Keywords

Poissonian pair correlationadditive energymetric number theory

Mathematics Subject Classification ID

Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Metric theory (11J83) General theory of distribution modulo (1) (11K06) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (13)

Remarks about inhomogeneous pair correlations ⋮ On exceptional sets in the metric Poissonian pair correlations problem ⋮ On the correlations of \(n^\alpha \bmod 1\) ⋮ THE PRIMES ARE NOT METRIC POISSONIAN ⋮ The metric theory of the pair correlation function of real-valued lacunary sequences ⋮ A pair correlation problem, and counting lattice points with the zeta function ⋮ A METRIC THEORY OF MINIMAL GAPS ⋮ Some negative results related to Poissonian pair correlation problems ⋮ A note on sequences not having metric Poissonian pair correlations ⋮ On the pair correlations of powers of real numbers ⋮ Pair correlation and equidistribution on manifolds ⋮ GCD sums and sum-product estimates ⋮ THERE IS NO KHINTCHINE THRESHOLD FOR METRIC PAIR CORRELATIONS

Cites Work

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• Refinements of Gál's theorem and applications
• GCD sums from Poisson integrals and systems of dilated functions
• The pair correlation function of fractional parts of polynomials
• Additive energy and the Hausdorff dimension of the exceptional set in metric pair correlation problems
• Large greatest common divisor sums and extreme values of the Riemann zeta function
• A Metrical Theorem in Diophantine Approximation
• A metric result on the pair correlation of fractional parts of sequences
• THE PRIMES ARE NOT METRIC POISSONIAN
• GCD sums and complete sets of square-free numbers
• DISTRIBUTION MODULO ONE AND RATNER’S THEOREM

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