Function fields in positive characteristic: Expansions and Cobhamʹs theorem

In the vein of Christol, Kamae, Mendès France and Rauzy, we consider the analogue of a problem of Mahler for rational functions in positive characteristic. To solve this question, we prove an extension of Cobhamʹs theorem for quasi-automatic functions and use the recent generalization of Christolʹs theorem obtained by Kedlaya.