The generalised Hausdorff measure of sets of Dirichlet non-improvable numbers

DOI10.1090/proc/16222OpenAlexW3094815969MaRDI QIDQ5880218

Philip Bos, Mumtaz Hussain, David Simmons

Publication date: 7 March 2023

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.14760

zbMATH Keywords

Diophantine approximationdimension functionHausdorff measurecontinued fractionszero-infinity law

Mathematics Subject Classification ID

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

Related Items (8)

A DIMENSIONAL RESULT ON THE PRODUCT OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS ⋮ Hausdorff measure of sets of Dirichlet non-improvable affine forms ⋮ A note on the relative growth of products of multiple partial quotients in the plane ⋮ Uniform Diophantine approximation with restricted denominators ⋮ Metrical properties of the large products of partial quotients in continued fractions ⋮ Hausdorff dimension for sets of continued fractions of formal Laurent series ⋮ Unnamed Item ⋮ Metrical properties for continued fractions of formal Laurent series

Cites Work

• Hausdorff measure of sets of Dirichlet non-improvable affine forms
• Metric properties of the product of consecutive partial quotients in continued fractions
• A mass transference principle and the Duffin-Schaeffer conjecture for Hausdorff measures
• HAUSDORFF MEASURE OF SETS OF DIRICHLET NON‐IMPROVABLE NUMBERS
• A zero-one law for improvements to Dirichlet’s Theorem
• An inhomogeneous Dirichlet theorem via shrinking targets
• The sets of Dirichlet non-improvable numbers versus well-approximable numbers
• A general principle for Hausdorff measure
• Uniformly non–improvable Dirichlet set via continued fractions
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