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| HAL: hal-00014580, version 1 |
| arXiv: math.NT/0511680 |
| Detailed view |  Export this paper |
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| On the Littlewood conjecture in fields of power series |
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| Boris Adamczewski 1Yann Bugeaud 2 |
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| (2005-11-28) |
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| Let $\k$ be an arbitrary field. For any fixed badly approximable power series $\Theta$ in $\k((X^{-1}))$, we give an explicit construction of continuum many badly approximable power series $\Phi$ for which the pair $(\Theta, \Phi)$ satisfies the Littlewood conjecture. We further discuss the Littlewood conjecture for pairs of algebraic power series. |
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| 1: | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| 2: | Institut de Recherche Mathématique Avancée (IRMA) |
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CNRS : UMR7501 – Université Louis Pasteur - Strasbourg I |
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| Subject | : | Mathematics/Number Theory |
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| Littlewood's conjecture – continued fractions – formal power series |
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| hal-00014580, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00014580 | |
| oai:hal.archives-ouvertes.fr:hal-00014580 | |
| From: Boris Adamczewski | |
| Submitted on: Monday, 28 November 2005 14:19:49 | |
| Updated on: Wednesday, 1 October 2008 15:03:47 | |
