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

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Kristensen, Simon (2003)
  • Subject: 11J13 | Mathematics - Number Theory | 11J83

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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