The Hausdorff measure version of Gallagher's theorem. Closing the gap and beyond

DOI10.1016/j.jnt.2017.09.027zbMath1455.11106arXiv1612.00139OpenAlexW2558547266MaRDI QIDQ1711700

Mumtaz Hussain, David Simmons

Publication date: 18 January 2019

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

Full work available at URL: https://arxiv.org/abs/1612.00139

zbMATH Keywords

metric Diophantine approximationHausdorff measure and dimensionJarník-type theoremsmultiplicative and inhomogeneous Diophantine approximation

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Metric theory (11J83)

Related Items (6)

JARNÍK TYPE THEOREMS ON MANIFOLDS ⋮ Effective equidistribution for multiplicative Diophantine approximation on lines ⋮ JARNÍK’S THEOREM WITHOUT THE MONOTONICITY ON THE APPROXIMATING FUNCTION ⋮ Higher-rank Bohr sets and multiplicative diophantine approximation ⋮ A NOTE ON MATRIX APPROXIMATION IN THE THEORY OF MULTIPLICATIVE DIOPHANTINE APPROXIMATION ⋮ MULTIPLICATIVE DIOPHANTINE APPROXIMATION OF THE EXPANSIONS UNDER DIFFERENT BASES ON A LINE

Cites Work

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• Multiplicatively badly approximable numbers and generalised Cantor sets
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• An inhomogeneous Jarník theorem
• A note on three problems in metric Diophantine approximation
• Multiplicative zero-one laws and metric number theory
• Measure theoretic laws for lim sup sets
• Schmidt's theorem, Hausdorff measures, and slicing
• Metric Simultaneous Diophantine Approximation

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