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

Research group:
TitleOn a problem in simultaneous Diophantine approximation: Schmidt's conjecture
Publication TypeJournal Article
Year of Publication2011
AuthorsBadziahin D, Pollington A, Velani S
JournalAnnals of Mathematics
Volume174
Pagination1837-1883
AbstractFor 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.
URLhttp://arxiv.org/abs/1001.2694
DOIhttp://dx.doi.org/10.4007/annals.2011.174.3.9

Edited 20 Oct 2011 - 17:41 by vb8

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