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

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

2003-06-26

arxiv.org/abs/math/0306377v4

Mathematics

Number Theory

Revised version

Scientific paper

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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