Sets of Dirichlet non-improvable numbers with certain order in the theory of continued fractions *

DOI10.1088/1361-6544/abe097zbMath1473.11153OpenAlexW3134068450MaRDI QIDQ5854647

Jian Xu, Jing Feng

Publication date: 17 March 2021

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6544/abe097

zbMATH Keywords

Hausdorff dimensioncontinued fractionsDirichlet non-improvable setproduct of partial quotients

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Fractals (28A80) Metric theory of continued fractions (11K50)

Related Items (4)

The growth speed for the product of consecutive digits in Lüroth expansions ⋮ A note on the relative growth of products of multiple partial quotients in the plane ⋮ Exact uniform approximation and Dirichlet spectrum in dimension at least two ⋮ Dimension theory of Lüroth digits

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the fast Khintchine spectrum in continued fractions
• On sums of degrees of the partial quotients in continued fraction expansions of Laurent series
• A localized Jarník-Besicovitch theorem
• Hausdorff dimension of certain sets arising in continued fraction expansions
• Sets of exact approximation order by rational numbers
• On simultaneous Diophantine approximations
• Metric properties of the product of consecutive partial quotients in continued fractions
• The relative growth rate for partial quotients in continued fractions
• A mass transference principle and the Duffin-Schaeffer conjecture for Hausdorff measures
• The relative growth rate for partial quotients
• Uniform Diophantine approximation related to -ary and -expansions
• A generalization of the Jarník–Besicovitch theorem by continued fractions
• HAUSDORFF MEASURE OF SETS OF DIRICHLET NON‐IMPROVABLE NUMBERS
• Measure theoretic laws for lim sup sets
• A zero-one law for improvements to Dirichlet’s Theorem
• Metrical Results on the Distribution of Fractional Parts of Powers of Real Numbers
• Sets of Fractional Dimensions (IV): On Rational Approximation to Real Numbers
• Dirichlet Uniformly Well-approximated Numbers
• Hausdorff dimension of an exceptional set in the theory of continued fractions
• 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
• A dimensional result in continued fractions

This page was built for publication: Sets of Dirichlet non-improvable numbers with certain order in the theory of continued fractions ^*