English

Classical metric Diophantine approximation revisited

Number Theory 2008-03-18 v1

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.

Keywords

Cite

@article{arxiv.0803.2351,
  title  = {Classical metric Diophantine approximation revisited},
  author = {Victor Beresnevich and Vasily Bernik and Maurice Dodson and Sanju Velani},
  journal= {arXiv preprint arXiv:0803.2351},
  year   = {2008}
}

Comments

31 pages, Dedicated to Klaus Roth on the occasion of his 80th birthday

R2 v1 2026-06-21T10:21:56.393Z