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.
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