Hausdorff dimension, lower order and Khintchine's theorem in metric Diophantine approximation.

DOI10.1515/crll.1992.432.69zbMath0749.11036OpenAlexW184042068MaRDI QIDQ4013264

Maurice M. Dodson

Publication date: 27 September 1992

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://www.digizeitschriften.de/dms/resolveppn/?PPN=GDZPPN002209977

zbMATH Keywords

Hausdorff dimensionmetric Diophantine approximationanalogue of Khintchine's theorem

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Metric theory (11J83) Diophantine approximation in probabilistic number theory (11K60)

Related Items (20)

Sets of exact approximation order by complex rational numbers ⋮ Multifractal analysis of the convergence exponent in continued fractions ⋮ A problem in non-linear Diophantine approximation ⋮ On simultaneous rational approximation to a real number and its integral powers. II. ⋮ Measure theoretic laws for limsup sets defined by rectangles ⋮ Mass transference principle for limsup sets generated by rectangles ⋮ Sets of exact approximation order by rational numbers ⋮ On sets of exact Diophantine approximation over the field of formal series ⋮ The sets of Dirichlet non-improvable numbers versus well-approximable numbers ⋮ A note on the theorem of Jarník-Besicovitch ⋮ An extension of quantitative nondivergence and applications to Diophantine exponents ⋮ Mass transference principle from rectangles to rectangles in Diophantine approximation ⋮ A shrinking target problem with target at infinity in rank one homogeneous spaces ⋮ Diophantine exponents and the Khintchine Groshev theorem ⋮ Going-up theorems for simultaneous Diophantine approximation ⋮ A general inhomogeneous Jarnik-Besicovitch theorem ⋮ Hausdorff dimension and uniform exponents in dimension two ⋮ The Mass Transference Principle: Ten years on ⋮ Explicit Salem sets and applications to metrical Diophantine approximation ⋮ THE DIFFERENCE BETWEEN THE HURWITZ CONTINUED FRACTION EXPANSIONS OF A COMPLEX NUMBER AND ITS RATIONAL APPROXIMATIONS

This page was built for publication: Hausdorff dimension, lower order and Khintchine's theorem in metric Diophantine approximation.