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ON THE LITTLEWOOD CONJECTURE IN SIMULTANEOUS DIOPHANTINE APPROXIMATION

Published online by Cambridge University Press:  24 April 2006

BORIS ADAMCZEWSKI  and
YANN BUGEAUD
BORIS ADAMCZEWSKI
Affiliation:
CNRS, Institut Camille Jordan, Université Claude Bernard Lyon 1, Bât. Braconnier, 21 avenue Claude Bernard, 69622 Villeurbanne cedex, Franceboris.adamczewski@math.univ-lyon1.fr
YANN BUGEAUD
Affiliation:
Université Louis Pasteur, UFR de mathématiques, 7, rue René Descartes, 67084 Strasbourg cedex, Francebugeaud@math.u-strasbg.fr
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Abstract

For any given real number $\alpha$ with bounded partial quotients, we construct explicitly continuum many real numbers $\beta$ with bounded partial quotients for which the pair $(\alpha, \beta)$ satisfies a strong form of the Littlewood conjecture. Our proof is elementary and rests on the basic theory of continued fractions.

Keywords

11J1311J70
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 73 , Issue 2 , April 2006 , pp. 355 - 366
Copyright
The London Mathematical Society 2006

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