A general inhomogeneous Jarnik-Besicovitch theorem

DOI10.1006/jnth.1998.2239zbMath0917.11036OpenAlexW2139064479MaRDI QIDQ1271158

Jason Levesley

Publication date: 20 July 1999

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1998.2239

zbMATH Keywords

Hausdorff dimensionresonant setubiquitous systeminhomogeneous diophantine approximationJarnik-Besicovitch theorem

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Diophantine approximation in probabilistic number theory (11K60) Inhomogeneous linear forms (11J20)

Related Items (12)

An inhomogeneous Jarník theorem ⋮ Metrical theorems on systems of affine forms ⋮ Measure theoretic laws for limsup sets defined by rectangles ⋮ A Survey on the Dimension Theory in Dynamical Diophantine Approximation ⋮ Badly approximable systems of affine forms ⋮ Diophantine approximation of the orbit of 1 in the dynamical system of beta expansions ⋮ Mass transference principle from rectangles to rectangles in Diophantine approximation ⋮ A NOTE ON INHOMOGENEOUS DIOPHANTINE APPROXIMATION IN BETA-DYNAMICAL SYSTEM ⋮ Sets with large intersection and ubiquity ⋮ A Fourier-analytic approach to inhomogeneous Diophantine approximation ⋮ The Mass Transference Principle: Ten years on ⋮ Explicit Salem sets and applications to metrical Diophantine approximation

Cites Work

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• The method of trigonometric sums in the metric theory of diophantine approximations of dependent quantities
• A Metrical Theorem in Diophantine Approximation
• Hausdorff dimension, lower order and Khintchine's theorem in metric Diophantine approximation.
• Diophantine approximation and a lower bound for Hausdorff dimension
• Geometric and probabilistic ideas in metric Diophantine approximation
• A note on the theorem of Jarník-Besicovitch
• Sets of Fractional Dimensions (IV): On Rational Approximation to Real Numbers
• Metrical Theorems on Fractional Parts of Sequences

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