Automata and transcendence in positive characteristic

We give a generalized and effective version of the Theorem of G. Christol, T. Kamae, M. Mendes France and G. Rauzy. By using this statement, we can pr ove transcendence results in the completion of the algebraic closure of a f unction 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. (C) 2000 Academic Press.