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On the Littlewood conjecture in simultaneous Diophantine approximation

Authors
  • Adamczewski, Boris
  • Bugeaud, Yann
Type
Published Article
Publication Date
Nov 28, 2005
Submission Date
Nov 28, 2005
Identifiers
arXiv ID: math/0511678
Source
arXiv
License
Unknown
External links

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.

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