Des crit\`eres de transcendance inspir\'es par un texte de Kolberg dat\'e de 1962

Abstract

Transcendence criteria inspired by Kolberg's paper dated 1962. In his paper dated 1962, Kolberg states and proves a theorem on the transcendence of the values of the sums of a class of certain power series in x, for algebraic values of x. It builds on Lindemann's theorem and uses, en passant, a transcendence criterion for the values of certain rational fonctions. This last criterion is made explicit. We clarify certain delicate points of the proof and show how to extend its scope.