Asymptotic behaviour for products of consecutive partial quotients in continued fractions

DOI10.1017/S000497272400025XMaRDI QIDQ6666597

Lei Shang, Xiao Chen, Junjie Li, Xin Zeng, Lulu Fang

Publication date: 20 January 2025

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Hausdorff dimensioncontinued fractionsresidual setsproduct of consecutive partial quotients

Mathematics Subject Classification ID

Fractals (28A80) Metric theory of continued fractions (11K50) Classification of real functions; Baire classification of sets and functions (26A21)

Cites Work

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• Diophantine approximation
• Metric properties of the product of consecutive partial quotients in continued fractions
• On the growth behavior of partial quotients in continued fractions
• HAUSDORFF MEASURE OF SETS OF DIRICHLET NON‐IMPROVABLE NUMBERS
• Extremely non-normal continued fractions
• A zero-one law for improvements to Dirichlet’s Theorem
• HAUSDORFF DIMENSION FOR THE SET OF POINTS CONNECTED WITH THE GENERALIZED JARNÍK–BESICOVITCH SET
• Big Birkhoff sums in $d$-decaying Gauss like iterated function systems
• Hausdorff dimension of an exceptional set in the theory of continued fractions
• SET OF EXTREMELY DIRICHLET NON-IMPROVABLE POINTS
• The sets of Dirichlet non-improvable numbers versus well-approximable numbers
• Uniformly non–improvable Dirichlet set via continued fractions
• Sets of Dirichlet non-improvable numbers with certain order in the theory of continued fractions ^*
• The generalised Hausdorff measure of sets of Dirichlet non-improvable numbers
• A note on the relative growth of products of multiple partial quotients in the plane
• Hausdorff dimension analysis of sets with the product of consecutive vs single partial quotients in continued fractions
• Hausdorff dimension of Dirichlet non-improvable set versus well-approximable set
• Baire category and the relative growth rate for partial quotients in continued fractions

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