Algebraic independence of certain Mahler numbers

In this note, we prove algebraic independence results for the values of a special class of Mahler functions. In particular, the generating functions of Thue–Morse, regular paperfolding and Cantor sequences belong to this class, and we obtain the algebraic independence of the values of these functions at every non-zero algebraic point in the open unit disk. The proof uses results on Mahler's method.

Independance algebrique des derivees d'une periode du module de Carlitz

We prove here that the p - 1 first derivatives of the fundamental period of the Carliz module are algebraically independent. For that purpose we will show to use Mahler's method in this situtaion.