Badly approximable systems of linear forms over a field of formal series
Journal de Théorie des Nombres de Bordeaux, Tome 18 (2006) no. 2, pp. 421-444.

Nous montrons que la dimension de Hausdorff de l’ensemble des systèmes mal approchables de m formes linéaires en n variables sur le corps des séries de Laurent à coefficients dans un corps fini est maximale. Ce résultat est un analogue de la généralisation multidimensionnelle de Schmidt du théorème de Jarník sur les nombres mal approchables.

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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DOI : https://doi.org/10.5802/jtnb.552
@article{JTNB_2006__18_2_421_0,
     author = {Simon Kristensen},
     title = {Badly approximable systems of linear forms over a field of formal series},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {421--444},
     publisher = {Universit\'e Bordeaux 1},
     volume = {18},
     number = {2},
     year = {2006},
     doi = {10.5802/jtnb.552},
     mrnumber = {2289432},
     zbl = {05135397},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.552/}
}
Simon Kristensen. Badly approximable systems of linear forms over a field of formal series. Journal de Théorie des Nombres de Bordeaux, Tome 18 (2006) no. 2, pp. 421-444. doi : 10.5802/jtnb.552. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.552/

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