Classical metric Diophantine approximation revisited

By Victor Beresnevich, V. Bernik, M. Dodson, Sanju Velani. 2008

71 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/83ba449f6374908de4b9756ec12eb0856cb315a0

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In Algebra and Number Theory

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Citations in the corpus

On shrinking targets for Z^m actions on tori (2008, background): “Rather surprisingly, Beresnevich et al [1] have shown that this result and, indeed, the dimension result of Bugeaud, Schmeling and Trubetskoy are consequences of the fact that for any irrational α and any x the inequality (3) has infinitely many solutions.”
Metric Diophantine Approximation : aspects of recent work (2016, background): “For further details, see [12, 13] and references within.”
Classical Metric Diophantine Approximation Revisited: The Khintchine–Groshev Theorem (2008, methodology): “For the sake of completeness, we mention that Theorems 4 and 5 are formally stated as Conjectures B and C in [1].”