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| HAL: hal-00705128, version 1 |
| DOI: 10.1016/j.jnt.2011.06.009 |
| Detailed view |  Export this paper |
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| Journal of Number Theory 132, 1 (2012) 1-25 |
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| Linear forms at a basis of an algebraic number field |
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| Bernard De Mathan 1 |
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| (2012-01-02) |
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| It was proved by Cassels and Swinnerton-Dyer that Littlewood conjecture in simultaneous Diophantine approximation holds for any pair of numbers in a cubic field. Later this result was generalized by Peck to a basis (1, α1 , * * * , αn ) of a real algebraic number field of degree at least 3. By transference, this result provides some solutions for the dual form of Littlewood's conjecture. Here we find another solutions, and using Baker's estimates for linear forms in logarithms of algebraic numbers, we discuss whether the result is best possible. |
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| 1: | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| Subject | : | Mathematics/Number Theory |
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| Attached file list to this document: | ||||||||||
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| hal-00705128, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00705128 | |
| oai:hal.archives-ouvertes.fr:hal-00705128 | |
| From: Bernard De Mathan | |
| Submitted on: Wednesday, 6 June 2012 21:11:58 | |
| Updated on: Thursday, 7 June 2012 08:58:28 | |
