GCD sums and sum-product estimates

DOI10.1007/s11856-019-1932-0zbMath1450.11094arXiv1806.07849OpenAlexW2978823444WikidataQ127112563 ScholiaQ127112563MaRDI QIDQ2303676

Thomas F. Bloom, Aled Walker

Publication date: 4 March 2020

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.07849

zbMATH Keywords

pair correlationsdistribution modulo 1GCD sumssum-product phenomenon

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Distribution modulo one (11J71) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

Related Items (10)

Remarks about inhomogeneous pair correlations ⋮ On the correlations of \(n^\alpha \bmod 1\) ⋮ On higher dimensional Poissonian pair correlation ⋮ A pair correlation problem, and counting lattice points with the zeta function ⋮ On some applications of GCD sums to arithmetic combinatorics ⋮ On a multi-dimensional Poissonian pair correlation concept and uniform distribution ⋮ A note on sequences not having metric Poissonian pair correlations ⋮ New expander bounds from affine group energy ⋮ THERE IS NO KHINTCHINE THRESHOLD FOR METRIC PAIR CORRELATIONS ⋮ Poissonian correlations of higher orders

Cites Work

• Lower bounds for the maximum of the Riemann zeta function along vertical lines
• Refinements of Gál's theorem and applications
• GCD sums from Poisson integrals and systems of dilated functions
• On the Minkowski distances and products of sum sets
• The pair correlation function of fractional parts of polynomials
• Additive energy and the Hausdorff dimension of the exceptional set in metric pair correlation problems
• On the Bogolyubov-Ruzsa lemma
• Large greatest common divisor sums and extreme values of the Riemann zeta function
• Sums Involving Common Divisors
• ADDITIVE ENERGY AND THE METRIC POISSONIAN PROPERTY
• THE PRIMES ARE NOT METRIC POISSONIAN
• GCD sums and complete sets of square-free numbers
• THERE IS NO KHINTCHINE THRESHOLD FOR METRIC PAIR CORRELATIONS
• Sommes de Gál et applications
• Variations on the Sum-Product Problem
• Unnamed Item

This page was built for publication: GCD sums and sum-product estimates