# Mesures d'indépendance linéaire simultanées sur les périodes d'intégrales abéliennes

Abstract : The purpose of this thesis is to obtain an effective demonstration of a result of Cohen, Shiga and Wolfart, which is a generalisation, in the case of Siegel spaces $\mathfrak{H}_{g}$ of arbitrary degree $g$, of the classical theorem of Schneider on the modular invariant $j(\tau)$. A first step in this direction consists, given an abelian variety$\mathcal{A}$ defined over $\overline{\mathbb{Q}}$ and parametrised by a point $\tau$ of the Siegel space, in giving a minoration of $|||\tau-\beta|||$, where $\beta$ is an algebraic point of the Siegel space, in terms of the geometrical data of the problem. To achieve this, we sharpen some tools of linear independence of logarithms of the Gel'fond-Baker's method.
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Theses
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https://tel.archives-ouvertes.fr/tel-00011233
Contributor : Eric Villani <>
Submitted on : Sunday, December 18, 2005 - 4:40:45 PM
Last modification on : Wednesday, December 9, 2020 - 3:08:58 PM
Long-term archiving on: : Friday, September 14, 2012 - 4:35:20 PM

### Identifiers

• HAL Id : tel-00011233, version 1

### Citation

Eric Villani. Mesures d'indépendance linéaire simultanées sur les périodes d'intégrales abéliennes. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2005. Français. ⟨tel-00011233⟩

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