Journal de Th´
eorie des Nombres
de Bordeaux
18
(2006), 421–444
Badly approximable systems of linear forms over
a field of formal series
par
Simon KRISTENSEN
R´esum´e. Nous montrons que la dimension de Hausdorff de l’en-semble des syst`emes mal approchables dem formes lin´eaires en nvariables sur le corps des s´eries de Laurent `a coefficients dans
un corps fini est maximale. Ce r´esultat est un analogue de la g´en´eralisation multidimensionnelle de Schmidt du th´eor`eme de Jarn´ık sur les nombres mal approchables.
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 an analogue of Schmidt’s multi-dimensional generalisation of Jarn´ık’s Theorem on badly approximable num-bers.
SimonKristensen
Department of Mathematical Sciences Faculty of Science
University of Aarhus Ny Munkegade, Building 530 8000 Aarhus C, Denmark
E-mail:[email protected]
