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| HAL : hal-00411418, version 1 |
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| The Riemann zeta function and related themes: papers in honour of Professor K. Ramachandra, National Institute for Advanced Studies (NIAS), Bangalore : India (2003) |
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| On Ramachandra's contributions to transcendental number theory |
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| Michel Waldschmidt 1 |
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| (2006) |
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| The title of this lecture refers to Ramachandra's paper in Acta Arithmetica [Ramachandra, 1968], which will be our central subject: in section 1 we state his Main Theorem, in section 2 we apply it to algebraically additive functions. Next we give new consequences of Ramachandra's results to density problems; for instance we discuss the following question: {\sl let $E$ be an elliptic curve which is defined over the field of algebraic numbers, and let $\Gamma$ be a finitely generated subgroup of algebraic points on $E$; is $\Gamma$ dense in $E(\bC)$ for the complex topology?} The other contributions of Ramachandra to transcendental number theory are dealt with more concisely in section 4. Finally we propose a few open problems. |
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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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| transcendental number theory – Schneider's method |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00411418, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00411418/fr/ | |
| oai:hal.archives-ouvertes.fr:hal-00411418_v1 | |
| Contributeur : Michel Waldschmidt | |
| Soumis le : Jeudi 27 Août 2009, 14:11:29 | |
| Dernière modification le : Jeudi 27 Août 2009, 14:26:07 | |
