The best Diophantine approximations: the phenomenon of degenerate dimension

2004/11/12 by Nikolai G Moshchevitin, Moshchevitin, Nikolai G · 1 citation
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0411293

27 pages

arxiv created 2004/11/12 · arxiv updated 2009/12/01

Abstract

This brief survey deals with multi-dimensional Diophantine approximations in sense of linear form and with simultaneous Diophantine approximations. We discuss the phenomenon of degenerate dimension of linear subspaces generated by the best Diophantine approximations. Originally most of these results have been established by the author in few years ago. Here we collect all of them together and give some new formulations.

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