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

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