Une version effective du th\'eor\`eme de Lindemann-Weierstrass par des m\'ethodes d'ind\'ependance alg\'ebrique

Abstract

We present a new completely effective proof of the Lindemann-Weierstrass theorem based on algebraic independence methods. Although it is slightly weaker than the best known estimate due to A. Sert, it improves the best estimate due to M. Ably obtained by such methods. The novelty of the proof lies in the simplicity of the construction of auxiliary functions, a fact that we exploit to introduce the non-specialist to methods of algebraic independence.