# On a problem in simultaneous Diophantine approximation: Schmidt's conjecture

Research group:
 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 1837-1883 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