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Badly approximable vectors, $C^{1}$ curves and number fields

Published online by Cambridge University Press:  11 February 2015

MANFRED EINSIEDLER
Affiliation:
ETH Zürich, Departement Mathematik, Rämistrasse 101 8092, Zürich, Switzerland email manfred.einsiedler@math.ethz.ch, beverly.lytle@math.ethz.ch
ANISH GHOSH
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India email ghosh@math.tifr.res.in
BEVERLY LYTLE
Affiliation:
ETH Zürich, Departement Mathematik, Rämistrasse 101 8092, Zürich, Switzerland email manfred.einsiedler@math.ethz.ch, beverly.lytle@math.ethz.ch

Abstract

We show that the set of points on $C^{1}$ curves which are badly approximable by rationals in a number field form a winning set in the sense of Schmidt. As a consequence, we obtain a number field version of Schmidt’s conjecture in Diophantine approximation.

Type
Research Article
Copyright
© Cambridge University Press, 2015 

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