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On a problem in simultaneous Diophantine approximation: Schmidt's conjecture by Badziahin, Dzmitry; Pollington, Andrew; Velani, Sanju is a scholarly article available to read on EtoBox.

What is On a problem in simultaneous Diophantine approximation: Schmidt's conjecture about?

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.

Author

Badziahin, Dzmitry; Pollington, Andrew; Velani, Sanju

Published

2010

Language

EN