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

Access Restriction
Open

 Author Badziahin, Dzmitry ♦ Pollington, Andrew ♦ Velani, Sanju Source arXiv.org Content type Text File Format PDF Date of Submission 2010-01-15 Language English
 Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics Subject Keyword Mathematics - Number Theory ♦ 11J25 ♦ math 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. Educational Use Research Learning Resource Type Article Page Count 43