  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.

Number Theory