Irrationality Measures and Transcendence in Positive Characteristic Original Research Article

We give a new criterion of transcendence in positive characteristic. This criterion is related to irrationality measure. It applies to give a new proof of the transcendency of ζ(s)/Πs (with an effective measure) for particular values of s, where ζ(s) is a Carlitz zeta value. The criterion also applies to new results, for instance the transcendency of some polynomial combinations of such quantities. The methods are elementary, and, essentially, use at once the degree and the order on K(T).