On a problem in simultaneous Diophantine approximation: Schmidt's conjecture
成果类型：
Article
署名作者：
Badziahin, Dzmitry; Pollington, Andrew; Velani, Sanju
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2011.174.3.9
发表日期：
2011
页码：
1837-1883
关键词：
摘要：
For any i, j >= 0 with i + j = 1, let Bad(i, j) denote the set of points (x, y) is an element of R-2 for which max{parallel to qx parallel to(1/i), parallel to qy parallel to(1/j)} > c/q for all q is an element of 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.