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

Simon Kristensen — 2006

Journal de Théorie des Nombres de Bordeaux

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 an analogue of Schmidt’s multi-dimensional generalisation of Jarník’s Theorem on badly approximable numbers.

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