Generalization of the criteria for linear independence of Nesterenko, Amoroso, Colmez, Fischler and Zudilin

摘要

Two different methods yield a criterion for linear independence due to Yu.V. Nesterenko. In the first part of this paper we use the original method due to Nesterenko and simplified by Amoroso and Colmez, and we refine the previous results for finite sets of complex numbers or elements in $mathbb{C}_p$.Next we use the method due to Fischler and Zudilin, which we already used in a previous paper, which works with infinite families of real or $p$–adic numbers in $mathbb{Q}_p$.