Classical metric Diophantine approximation revisited

2008/03/16 by Victor Beresnevich, Beresnevich, Victor, Vasily Bernik +5 · 3 citations
Mathematics · #11J83 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0803.2351

openalex publication_date 2008/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The idea of using measure theoretic concepts to investigate the size of number theoretic sets, originating with E. Borel, has been used for nearly a century. It has led to the development of the theory of metrical Diophantine approximation, a branch of Number Theory which draws on a rich and broad variety of mathematics. We discuss some recent progress and open problems concerning this classical theory. In particular, generalisations of the Duffin-Schaeffer and Catlin conjectures are formulated and explored.

Citations

• Khintchine’s problem in metric Diophantine approximation

Cited by

• Khintchine's theorem and Diophantine approximation on manifolds
• The dimension of well approximable numbers
• On shrinking targets for Z^m actions on tori

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• Projective metric number theory
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