
On a problem in simultaneous Diophantine approximation: Schmidt's conjecture
Title  On a problem in simultaneous Diophantine approximation: Schmidt's conjecture 
Publication Type  Journal Article 
Year of Publication  2011 
Authors  Badziahin D, Pollington A, Velani S 
Journal  Annals of Mathematics 
Volume  174 
Pagination  18371883 
Abstract  For any $i,j \ge 0$ with $i+j =1$, let bad$(i,j)$ denote the set of points $(x,y) \in R^2$ for which $ \max \{\qx\^{1/i}, \qy\^{1/j} \} > c/q $ for all $ q \in N $. Here $c = c(x,y)$ is a positive constant. Our main result implies that any finite intersection of such sets has full dimension. This settles a conjecture of Wolfgang M. Schmidt in the theory of simultaneous Diophantine approximation.

URL  http://arxiv.org/abs/1001.2694 
DOI  http://dx.doi.org/10.4007/annals.2011.174.3.9 
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Edited 20 Oct 2011  17:41 by vb8
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