Metric properties of the product of consecutive partial quotients in continued fractions

DOI10.1007/s11856-020-2049-1zbMath1452.11095OpenAlexW3045868847MaRDI QIDQ2200062

Jian Xu, Jun Wu, Ling-ling Huang

Publication date: 15 September 2020

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11856-020-2049-1

zbMATH Keywords

continued fraction expansionsHausdorff dimensionHölder exponentLebesgue measureDiophantine approximations\(\phi\)-Dirichlet improvable numbers

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Metric theory (11J83) Metric theory of continued fractions (11K50)

Related Items (15)

The generalised Hausdorff measure of sets of Dirichlet non-improvable numbers ⋮ A DIMENSIONAL RESULT ON THE PRODUCT OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS ⋮ On the relative growth rate of the product of consecutive partial quotients in continued fraction expansions of Laurent series ⋮ A note on the relative growth of products of multiple partial quotients in the plane ⋮ The distribution of the large partial quotients in continued fraction expansions ⋮ Hausdorff dimension analysis of sets with the product of consecutive vs single partial quotients in continued fractions ⋮ Metrical properties of the large products of partial quotients in continued fractions ⋮ Metrical properties for the weighted sums of degrees of multiple partial quotients in continued fractions of Laurent series ⋮ Hausdorff dimension for sets of continued fractions of formal Laurent series ⋮ Metrical properties for functions of consecutive multiple partial quotients in continued fractions ⋮ Unnamed Item ⋮ Metrical properties for continued fractions of formal Laurent series ⋮ 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 ⋮ HAUSDORFF DIMENSION FOR THE SET OF POINTS CONNECTED WITH THE GENERALIZED JARNÍK–BESICOVITCH SET

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