Bohr sets and multiplicative Diophantine approximation

DOI10.1215/00127094-2018-0001zbMath1401.11116arXiv1703.07016OpenAlexW2609135235MaRDI QIDQ1653120

Sam Chow

Publication date: 17 July 2018

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.07016

zbMATH Keywords

Littlewood's conjectureadditive combinatoricsDuffin-Schaeffer conjectureinhomogeneous Diophantine approximationbadly approximable numbersLiouville numbersmetric number theoryBohr setsDuffin-Schaeffer theoremGallagher's Theoremmultiplicative Diophantine approximation

Mathematics Subject Classification ID

Lattices and convex bodies (number-theoretic aspects) (11H06) Metric theory (11J83) Lattices and convex bodies in (2) dimensions (aspects of discrete geometry) (52C05) Inhomogeneous linear forms (11J20)

Related Items (12)

Density of oscillating sequences in the real line ⋮ On the metric theory of inhomogeneous Diophantine approximation: an Erdős-Vaaler type result ⋮ FULLY INHOMOGENEOUS MULTIPLICATIVE DIOPHANTINE APPROXIMATION OF BADLY APPROXIMABLE NUMBERS ⋮ Counting multiplicative approximations ⋮ JARNÍK TYPE THEOREMS ON MANIFOLDS ⋮ On the metric theory of multiplicative Diophantine approximation ⋮ Effective equidistribution for multiplicative Diophantine approximation on lines ⋮ THERE IS NO KHINTCHINE THRESHOLD FOR METRIC PAIR CORRELATIONS ⋮ A Fourier-analytic approach to inhomogeneous Diophantine approximation ⋮ Higher-rank Bohr sets and multiplicative diophantine approximation ⋮ A NOTE ON MATRIX APPROXIMATION IN THE THEORY OF MULTIPLICATIVE DIOPHANTINE APPROXIMATION ⋮ The divergence Borel-Cantelli Lemma revisited

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