Hausdorff measure of sets of Dirichlet non-improvable affine forms

DOI10.1016/j.aim.2022.108353zbMath1496.11096arXiv2006.05727OpenAlexW3034939238MaRDI QIDQ2143654

Wooyeon Kim, Taehyeong Kim

Publication date: 31 May 2022

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.05727

zbMATH Keywords

inhomogeneous Diophantine approximationDirichlet's theoremshrinking targetslocal ubiquityspace of grids

Mathematics Subject Classification ID

Diophantine approximation in probabilistic number theory (11K60) Homogeneous flows (37A17) Inhomogeneous linear forms (11J20)

Related Items (5)

The generalised Hausdorff measure of sets of Dirichlet non-improvable numbers ⋮ A measure estimate in geometry of numbers and improvements to Dirichlet's theorem ⋮ Generalised Hausdorff measure of sets of Dirichlet non-improvable matrices in higher dimensions ⋮ Metrical properties of the large products of partial quotients in continued fractions ⋮ Hausdorff dimension for sets of continued fractions of formal Laurent series

Cites Work

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• A solution to a problem of Cassels and Diophantine properties of cubic numbers
• Singular systems of linear forms and non-escape of mass in the space of lattices
• Logarithm laws for flows on homogeneous spaces
• An inhomogeneous Jarník theorem
• Badly approximable systems of affine forms
• Metrical theorems on systems of affine forms
• Mass transference principle from rectangles to rectangles in Diophantine approximation
• Ubiquity and a general logarithm law for geodesics
• Badly approximable systems of affine forms, fractals, and Schmidt games
• A mass transference principle for systems of linear forms and its applications
• HAUSDORFF MEASURE OF SETS OF DIRICHLET NON‐IMPROVABLE NUMBERS
• An Introduction to the Geometry of Numbers
• Measure theoretic laws for lim sup sets
• Classical Metric Diophantine Approximation Revisited: The Khintchine-Groshev Theorem
• Divergent trajectories of flows on homogeneous spaces and Diophantine approximation.
• Diophantine approximation and a lower bound for Hausdorff dimension
• Hausdorff measure and linear forms.
• Exponents of Diophantine Approximation
• Diophantine approximation for products of linear maps — logarithmic improvements
• A zero-one law for improvements to Dirichlet’s Theorem
• An inhomogeneous Dirichlet theorem via shrinking targets
• Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents
• Hausdorff dimension of an exceptional set in the theory of continued fractions
• TRANSFERENCE THEOREMS FOR DIOPHANTINE APPROXIMATION WITH WEIGHTS
• The sets of Dirichlet non-improvable numbers versus well-approximable numbers
• Dimension Bound for Badly Approximable Grids
• Diophantine Approximation and Hausdorff Dimension
• The generalised Hausdorff measure of sets of Dirichlet non-improvable numbers
• A measure estimate in geometry of numbers and improvements to Dirichlet's theorem

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