Generalised Hausdorff measure of sets of Dirichlet non-improvable matrices in higher dimensions

DOI10.1007/s40993-023-00436-yzbMath1528.11060arXiv2201.03062OpenAlexW4383217582MaRDI QIDQ6132976

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Publication date: 21 July 2023

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

Full work available at URL: https://arxiv.org/abs/2201.03062

zbMATH Keywords

Hausdorff dimensionHausdorff measureDirichlet's theoremDiophantine approximationsshrinking target problem

Mathematics Subject Classification ID

Metric theory (11J83) Diophantine approximation in probabilistic number theory (11K60)

Cites Work

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• Dirichlet's theorem on Diophantine approximation and homogeneous flows
• Logarithm laws for flows on homogeneous spaces
• Hausdorff measure of sets of Dirichlet non-improvable affine forms
• Ubiquity and a general logarithm law for geodesics
• A mass transference principle for systems of linear forms and its applications
• 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.
• Khintchine-type theorems on manifolds
• A zero-one law for improvements to Dirichlet’s Theorem
• An inhomogeneous Dirichlet theorem via shrinking targets
• Diophantine Approximation and Hausdorff Dimension

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