  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.
