Automata and Transcendence in Positive Characteristic Original Research Article

We give a generalized and effective version of the Theorem of G. Christol, T. Kamae, M. Mendès France and G. Rauzy. By using this statement, we can prove transcendence results in the completion of the algebraic closure of a function field of positive characteristic. We also obtain weak transcendence statements, i.e., for certain sequences in a function field, the existence of an isomorphism from this function field, which transforms the sequence into a sequence with a transcendental limit.