Badly approximable systems of linear forms over a field of formal series

2003/06/26 by Simon Kristensen, Kristensen, Simon
Mathematics · #11J13 #11J83 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11J13 #msc:11J83

paper · pdf · doi:10.48550/arxiv.math/0306377

Revised version

arxiv created 2004/08/05 · arxiv updated 2009/11/30

Abstract

We prove that the Hausdorff dimension of the set of badly approximable systems of m linear forms in n variables over the field of Laurent series with coefficients from a finite field is maximal. This is a analogue of Schmidt's multi-dimensional generalisation of Jarnik's Theorem on badly approximable numbers.

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