Uniformly non–improvable Dirichlet set via continued fractions

DOI10.1090/proc/14587zbMath1431.11100OpenAlexW2915415525WikidataQ128335368 ScholiaQ128335368MaRDI QIDQ5234957

Jun Wu, Ling-ling Huang

Publication date: 7 October 2019

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

Full work available at URL: https://doi.org/10.1090/proc/14587

zbMATH Keywords

Hausdorff dimensioncontinued fractionpartial quotients

Mathematics Subject Classification ID

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

Related Items (12)

The generalised Hausdorff measure of sets of Dirichlet non-improvable numbers ⋮ A DIMENSIONAL RESULT ON THE PRODUCT OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS ⋮ 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 ⋮ Hausdorff dimension of an exceptional set in the theory of continued fractions ⋮ Hausdorff dimension for sets of continued fractions of formal Laurent series ⋮ Metric properties of the product of consecutive partial quotients in continued fractions ⋮ ON THE LONGEST BLOCK FUNCTION IN CONTINUED FRACTIONS ⋮ The sets of Dirichlet non-improvable numbers versus well-approximable numbers ⋮ Dimension theory of the product of partial quotients in Lüroth expansions ⋮ Sets of Dirichlet non-improvable numbers with certain order in the theory of continued fractions ^* ⋮ Limit theorems for sums of products of consecutive partial quotients of continued fractions

Cites Work

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• Hausdorff dimension of certain sets arising in continued fraction expansions
• The relative growth rate for partial quotients
• HAUSDORFF MEASURE OF SETS OF DIRICHLET NON‐IMPROVABLE NUMBERS
• On Khintchine exponents and Lyapunov exponents of continued fractions
• On the fractional dimension of sets of continued fractions
• A zero-one law for improvements to Dirichlet’s Theorem
• A dimensional result in continued fractions
• The relative growth rate of the largest partial quotient to the sum of partial quotients in continued fraction expansions

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