Sets of exact approximation order by rational numbers

DOI10.1007/s00208-003-0445-6zbMath1044.11059OpenAlexW1996982583MaRDI QIDQ1411999

Yann Bugeaud

Publication date: 4 November 2003

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-003-0445-6

zbMATH Keywords

Hausdorff measureapproximation order by rational numbers

Mathematics Subject Classification ID

Homogeneous approximation to one number (11J04)

Related Items (20)

Sets of exact approximation order by complex rational numbers ⋮ A DIMENSIONAL RESULT ON THE PRODUCT OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS ⋮ The growth speed for the product of consecutive digits in Lüroth expansions ⋮ A note on approximation efficiency and partial quotients of Engel continued fractions ⋮ A localized Jarník-Besicovitch theorem ⋮ Exact approximation order and well-distributed sets ⋮ Linear forms of a given Diophantine type ⋮ Diophantine approximations. Abstracts from the workshop held April 17--23, 2022 ⋮ Metric results on sumsets and Cartesian products of classes of Diophantine sets ⋮ On sets of exact Diophantine approximation over the field of formal series ⋮ Sharpness results concerning finite differences in Fourier analysis on the circle group ⋮ Diophantine approximation and Cantor sets ⋮ On the intersections of localized Jarník sets and localized uniformly Jarník sets in continued fractions ⋮ Irrationality exponent, Hausdorff dimension and effectivization ⋮ A generalization of the Jarník–Besicovitch theorem by continued fractions ⋮ The relative growth rate for partial quotients in continued fractions ⋮ A classification of aperiodic order via spectral metrics and Jarník sets ⋮ A dimensional result in continued fractions ⋮ Sets of Dirichlet non-improvable numbers with certain order in the theory of continued fractions ^* ⋮ EXACT DIMENSIONS OF EXCEPTIONAL SETS IN LÜROTH EXPANSIONS

Cites Work

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• Diophantine approximations and diophantine equations
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• An inhomogeneous Jarník theorem
• Hausdorff dimension, lower order and Khintchine's theorem in metric Diophantine approximation.
• A note on the theorem of Jarník-Besicovitch
• Hausdorff measure and linear forms.
• Sets of Fractional Dimensions (IV): On Rational Approximation to Real Numbers
• Sets of exact `logarithmic' order in the theory of Diophantine approximation

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