The Duffin-Schaeffer conjecture with extra divergence. II

DOI10.1007/s00209-012-1126-5zbMath1333.11068arXiv1201.1210OpenAlexW2002303912WikidataQ122863874 ScholiaQ122863874MaRDI QIDQ379237

Glyn Harman, Victor V. Beresnevich, Alan K. Haynes, Sanju L. Velani

Publication date: 11 November 2013

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

Full work available at URL: https://arxiv.org/abs/1201.1210

zbMATH Keywords

diophantine approximationDuffin-Schaeffer conjecturemetric number theory

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 (17)

Liminf sets in simultaneous Diophantine approximation ⋮ Bohr sets and multiplicative Diophantine approximation ⋮ On the metric theory of inhomogeneous Diophantine approximation: an Erdős-Vaaler type result ⋮ Variations autour d'un théorème métrique de Khintchine ⋮ Rational approximations of irrational numbers ⋮ On the Duffin-Schaeffer conjecture ⋮ KHINTCHINE'S THEOREM WITH RANDOM FRACTIONS ⋮ Counterexamples, covering systems, and zero-one laws for inhomogeneous approximation ⋮ The Duffin–Schaeffer theorem in number fields ⋮ The Duffin-Schaeffer conjecture with extra divergence ⋮ JARNÍK’S THEOREM WITHOUT THE MONOTONICITY ON THE APPROXIMATING FUNCTION ⋮ SOME REFINED RESULTS ON THE MIXED LITTLEWOOD CONJECTURE FOR PSEUDO-ABSOLUTE VALUES ⋮ THE DUFFIN–SCHAEFFER‐TYPE CONJECTURES IN VARIOUS LOCAL FIELDS ⋮ A Fourier-analytic approach to inhomogeneous Diophantine approximation ⋮ Higher-rank Bohr sets and multiplicative diophantine approximation ⋮ Variants of Khintchine's theorem in metric Diophantine approximation ⋮ On metric theory of Diophantine approximation for complex numbers

Cites Work

• Approximation by reduced fractions
• On the metric theory of diophantine approximation
• A mass transference principle and the Duffin-Schaeffer conjecture for Hausdorff measures
• On the distribution of the convergents of almost all real numbers
• Khintchine's problem in metric diophantine approximation
• The k ‐dimensional Duffin and Schaeffer conjecture
• The Duffin-Schaeffer conjecture with extra divergence
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