The sets of Dirichlet non-improvable numbers versus well-approximable numbers

DOI10.1017/etds.2019.41zbMath1455.11111arXiv1806.00618OpenAlexW2963513284WikidataQ114119511 ScholiaQ114119511MaRDI QIDQ5131212

Ayreena Bakhtawar, Philip Bos, Mumtaz Hussain

Publication date: 4 November 2020

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.00618

zbMATH Keywords

Hausdorff dimensionDirichlet's theoremJarnik theoremuniform Diophantine approximation

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Metric theory (11J83) Metric theory of continued fractions (11K50) Diophantine approximation in probabilistic number theory (11K60)

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 ⋮ 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 ⋮ Hausdorff dimension analysis of sets with the product of consecutive vs single partial quotients in continued fractions ⋮ Uniform Diophantine approximation with restricted denominators ⋮ Metrical properties of the large products of partial quotients in continued fractions ⋮ Hausdorff dimension of an exceptional set in the theory of continued fractions ⋮ Hausdorff dimension of Dirichlet non-improvable set versus well-approximable set ⋮ Hausdorff dimension for sets of continued fractions of formal Laurent series ⋮ Metrical properties for continued fractions of formal Laurent series ⋮ Sets of Dirichlet non-improvable numbers with certain order in the theory of continued fractions ^* ⋮ METRICAL PROBLEMS IN DIOPHANTINE APPROXIMATION ⋮ 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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