# Propriétés diophantiennes de la fonction zêta de Riemann aux entiers impairs

Abstract : This thesis deals with the arithmetical study of the values of the Riemann zeta function at odd integers. Four results are proved : - Let $a$ be a rational number, $\vert a \vert <1$. The Q-vector space spanned by $1, Li_1(a), Li_2(a),...$ has infinite dimension. - The Q-vector space spanned by $1, \zeta(3), \zeta(5), \zeta(7),...$ has infinite dimension. - There exists an odd integer $j$, $5\le j \le 169$ such that $1, \zeta(3), \zeta(j)$ are linearly independent over Q. - At least one among the nine numbers $\zeta(5), \zeta(7),..., \zeta(21)$ is irrational.
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Document type :
Theses
Mathématiques [math]. Université de Caen, 2001. Français
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https://tel.archives-ouvertes.fr/tel-00004519
Contributor : Tanguy Rivoal <>
Submitted on : Thursday, February 5, 2004 - 2:14:26 PM
Last modification on : Friday, February 10, 2017 - 3:18:57 PM
Document(s) archivé(s) le : Tuesday, September 7, 2010 - 4:55:52 PM

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• HAL Id : tel-00004519, version 1

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Tanguy Rivoal. Propriétés diophantiennes de la fonction zêta de Riemann aux entiers impairs. Mathématiques [math]. Université de Caen, 2001. Français. <tel-00004519>

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