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| HAL : hal-00407199, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Report on some recent advances in Diophantine approximation |
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| Michel Waldschmidt 1 |
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| (24/07/2009) |
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| A basic question of Diophantine approximation, which is the first issue we discuss, is to investigate the rational approximations to a single real number. Next, we consider the algebraic or polynomial approximations to a single complex number, as well as the simultaneous approximation of powers of a real number by rational numbers with the same denominator. Finally we study generalisations of these questions to higher dimensions. Several recent advances have been made by B.~Adamczewski, Y.~Bugeaud, S.~Fischler, M.~Laurent, T.~Rivoal, D.~Roy and W.M.~Schmidt, among others. We review some of these works. |
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| 1 : | Institut de Mathématiques de Jussieu (IMJ) |
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CNRS : UMR7586 – Université Pierre et Marie Curie - Paris VI – Université Paris-Diderot - Paris VII |
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| Domaine | : | Mathématiques/Théorie des nombres |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00407199, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00407199/fr/ | |
| oai:hal.archives-ouvertes.fr:hal-00407199_v1 | |
| Contributeur : Michel Waldschmidt | |
| Soumis le : Vendredi 24 Juillet 2009, 10:22:26 | |
| Dernière modification le : Vendredi 24 Juillet 2009, 14:23:51 | |
