Abstract Let K be a finite field, ( x ) the field of rational functions in over and K formal power series . We show that under certain conditions integral combinations with algebraic coefficients U 1 -number are m -numbers , where is degree extension ), determined by these c...

In 1980, Christol, Kamae, Mendès France and Rauzy stated in [3] an important theorem in automata theory. This theorem links sequences recognized by automata and algebraic formal power series. In 1994, Bruyère, Hansel, Michaux and Villemaire extended this theorem with a logical link in [2]. With theses two articles, we can translate the property for a formal power series to be algebraic in combi...

There is a theory of continued fractions for formal power series in x−1 with coefficients in a field Fq. This theory bears a close analogy with classical continued fractions for real numbers with formal power series playing the role of real numbers and the sum of the terms of non-negative degree in x playing the role of the integral part. In this paper we give a family of formal power series in...