Badly approximable systems of linear forms over a field of formal series
- [1] Department of Mathematical Sciences Faculty of Science University of Aarhus Ny Munkegade, Building 530 8000 Aarhus C, Denmark
Journal de Théorie des Nombres de Bordeaux (2006)
- Volume: 18, Issue: 2, page 421-444
- ISSN: 1246-7405
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topKristensen, Simon. "Badly approximable systems of linear forms over a field of formal series." Journal de Théorie des Nombres de Bordeaux 18.2 (2006): 421-444. <http://eudml.org/doc/249662>.
@article{Kristensen2006,
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 Jarník’s Theorem on badly approximable numbers.},
affiliation = {Department of Mathematical Sciences Faculty of Science University of Aarhus Ny Munkegade, Building 530 8000 Aarhus C, Denmark},
author = {Kristensen, Simon},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Laurent series; badly approximable systems; -games; Hausdorff dimension; Jarnik's theorem},
language = {eng},
number = {2},
pages = {421-444},
publisher = {Université Bordeaux 1},
title = {Badly approximable systems of linear forms over a field of formal series},
url = {http://eudml.org/doc/249662},
volume = {18},
year = {2006},
}
TY - JOUR
AU - Kristensen, Simon
TI - Badly approximable systems of linear forms over a field of formal series
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2006
PB - Université Bordeaux 1
VL - 18
IS - 2
SP - 421
EP - 444
AB - 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.
LA - eng
KW - Laurent series; badly approximable systems; -games; Hausdorff dimension; Jarnik's theorem
UR - http://eudml.org/doc/249662
ER -
References
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