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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


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