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arXiv · 0803.2351

Classical metric Diophantine approximation revisited

Victor Beresnevich·Vasily Bernik·Maurice Dodson·Sanju Velani
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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.

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Victor Beresnevich, Vasily Bernik, Maurice Dodson, Sanju Velani. 2008-03-16. Classical metric Diophantine approximation revisited. https://arxiv.org/abs/0803.2351

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