Mesure d'indépendance linéaire de logarithmes dans un groupe algébrique commutatif

Abstract

We obtain some new results in the theory of linear forms in logarithms on a commutative algebraic group, defined over $\text{Q}$. We generalize recent progress of S. David and N. Hirata [1]. In particular, we achieve an optimal linear independence measure in the height of the linear form and a measure more precise than Hirata's [4] for parameters related to the logarithms. The proof rests on Baker's method and a new argument of arithmetical nature.