On a problem in simultaneous Diophantine approximation: Littlewood's conjecture

DOI10.1007/BF02392812zbMath0970.11026OpenAlexW2089575867WikidataQ123193256 ScholiaQ123193256MaRDI QIDQ5928897

Andrew D. Pollington, Sanju L. Velani

Publication date: 19 June 2001

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02392812

zbMATH Keywords

Borel-Cantelli lemmaCantor-type setHausdorff dimensionLittlewood's conjecture

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Simultaneous homogeneous approximation, linear forms (11J13) Metric theory (11J83)

Related Items (17)

On the complexity of a putative counterexample to the -adic Littlewood conjecture ⋮ Reversals and palindromes in continued fractions ⋮ Multiplicatively badly approximable matrices up to logarithmic factors ⋮ Diophantine approximation for products of linear maps — logarithmic improvements ⋮ FULLY INHOMOGENEOUS MULTIPLICATIVE DIOPHANTINE APPROXIMATION OF BADLY APPROXIMABLE NUMBERS ⋮ Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation ⋮ Effective equidistribution for multiplicative Diophantine approximation on lines ⋮ On the mixed Littlewood conjecture and continued fractions in quadratic fields ⋮ The Littlewood conjecture and linear recurrences ⋮ On a problem in simultaneous Diophantine approximation: Schmidt's conjecture ⋮ Perfectly ordered quasicrystals and the Littlewood conjecture ⋮ Metrical musings on Littlewood and friends ⋮ Badly approximable numbers and Littlewood-type problems ⋮ A generalization of the Jarník–Besicovitch theorem by continued fractions ⋮ The work of Einsiedler, Katok and Lindenstrauss on the Littlewood conjecture ⋮ Metric Diophantine Approximation—From Continued Fractions to Fractals ⋮ Fourier transforms of Gibbs measures for the Gauss map

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Simultaneous rational approximations to algebraic numbers
• Continued fractions and Fourier transforms
• Metric Simultaneous Diophantine Approximation
• On the product of three homogeneous linear forms and indefinite ternary quadratic forms

This page was built for publication: On a problem in simultaneous Diophantine approximation: Littlewood's conjecture