HYPERQUADRATIC CONTINUED FRACTIONS AND AUTOMATIC SEQUENCES

Alain Lasjaunias (1) , Jia-Yan Yao (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 THU - Tsinghua University [Beijing]

The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. This connection is illustrated by three families of examples and a counterexample.

Domaines: Théorie des nombres [math.NT]

Alain Lasjaunias, Jia-Yan Yao. HYPERQUADRATIC CONTINUED FRACTIONS AND AUTOMATIC SEQUENCES. 2015. ⟨hal-01260584⟩