On certain recurrent and automatic sequences in finite fields

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

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

In this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field of characteristic $2$, recently introduced by the first author in connection with algebraic continued fractions. By including it in a large family of recurrent sequences in an arbitrary finite field, we prove its automaticity. Then we give a criterion on automatic sequences, generalizing a previous result and this allows us to present new families of automatic sequences in an arbitrary finite field.

Domaines: Théorie des nombres [math.NT]

Alain Lasjaunias, Jia-Yan Yao. On certain recurrent and automatic sequences in finite fields. 2016. ⟨hal-01313548⟩