G\'en\'eralisations Quantitatives du Crit\'ere D'ind\'ependance Lin\'eaire De Nesterenko

Abstract

In this paper we extend Fischler's quantitative generalization of Nesterenko's linear independence criterion, by weakening the hypotheses on the divisors of the coe cients of the linear forms and allowing (to some extent) the linear forms not to tend to 0. Another version of this result is proved, in the spirit of Siegel's criterion, with a recurrence relation veri ed by the linear forms. Finally, the results are restated in a more general setting in terms of convex bodies and lattices of $\mathbb{R}^n$.