Mesures de transcendance pour les points algébriques de fonctions modulaires de Siegel

Abstract

We give an effective version of a result of Cohen, Shiga and Wolfart, which is a generalisation to the case of Siegel spaces of arbitrary degree, of the classical theorem of Schneider on the modular invariant j ( τ ) . Given a point τ of the Siegel space parameterizing a principally polarised Abelian variety A defined over Q ¯ , we obtain a lower bound for the distance between τ and algebraic points β of the Siegel space, in terms of the geometrical data of the problem. To achieve this, we establish a simultaneous measure of linear independence for periods of Abelian integrals, using Baker's method. To cite this article: E. Villani, C. R. Acad. Sci. Paris, Ser. I 344 (2007).