Abstract
For any i;j > 0 with i + j = 1, let Bad(i;j) denote the set of points (x;y) 2 R 2 for which maxfkqxk 1=i ; kqyk 1=j g > c=q for all q 2 N. Here c = c(x;y) is a positive constant. Our main result implies that any nite intersection of such sets has full dimension. This settles a conjecture of Wolfgang M. Schmidt in the theory of simultaneous Diophantine approximation.
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