GCD sums and complete sets of square-free numbers

DOI10.1112/blms/bdu094zbMath1375.11055arXiv1402.0249OpenAlexW2006086945MaRDI QIDQ5173345

Kristian Seip, Andriy V. Bondarenko

Publication date: 9 February 2015

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.0249

zbMATH Keywords

greatest common divisors (GCD) matricesgreatest common divisors (GCD) sums

Mathematics Subject Classification ID

(H^p)-spaces (42B30) Convergence and absolute convergence of Fourier and trigonometric series (42A20) Irregularities of distribution, discrepancy (11K38) Matrices, determinants in number theory (11C20)

Related Items (17)

Gál-type GCD sums beyond the critical line ⋮ Lower bounds for the maximum of the Riemann zeta function along vertical lines ⋮ ADDITIVE ENERGY AND THE METRIC POISSONIAN PROPERTY ⋮ Refinements of Gál's theorem and applications ⋮ On exceptional sets in the metric Poissonian pair correlations problem ⋮ Additive energy and the Hausdorff dimension of the exceptional set in metric pair correlation problems ⋮ Extreme values of derivatives of the Riemann zeta function ⋮ Some open questions in analysis for Dirichlet series ⋮ The distribution of values of zeta and \(L\)-functions ⋮ An arithmetical approach to the convergence problem of series of dilated functions and its connection with the Riemann zeta function ⋮ Note on the Resonance Method for the Riemann Zeta Function ⋮ A METRIC THEORY OF MINIMAL GAPS ⋮ New Computations of the Riemann Zeta Function on the Critical Line ⋮ On a multi-dimensional Poissonian pair correlation concept and uniform distribution ⋮ An optimization problem concerning multiplicative functions ⋮ GCD sums and sum-product estimates ⋮ Convergence of series of dilated functions and spectral norms of GCD matrices

Cites Work

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• On series \(\sum c_k f(kx)\) and Khinchin's conjecture
• GCD sums from Poisson integrals and systems of dilated functions
• An arithmetical mapping and applications to Ω-results for the Riemann zeta function
• Sums Involving Common Divisors
• Some theorems in the metric theory of diophantine approximation
• SOME CASES OF THE DUFFIN AND SCHAEFFER CONJECTURE
• Note on some greatest common divisor matrices
• Diophantine Approximations and Hilbert's Space

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