A NOTE ON HYPERQUADRATIC CONTINUED FRACTIONS IN CHARACTERISTIC 2 WITH PARTIAL QUOTIENTS OF DEGREE 1

A Lasjaunias (1)

1 IMB - Institut de Mathématiques de Bordeaux

In this note, we describe a family of particular algebraic, and nonquadratic, power series over an arbitrary finite field of characteristic 2, having a continued fraction expansion with all partial quotients of degree one. The main purpose being to point out a common origin with another analogue family in odd characteristic, which has been studied in [LY1].

Mots clés: Continued fractions; Fields of power series; Finite fields 2000 Mathematics Subject Classification: 11J70; 11T55

Domaines: Théorie des nombres [math.NT]

A Lasjaunias. A NOTE ON HYPERQUADRATIC CONTINUED FRACTIONS IN CHARACTERISTIC 2 WITH PARTIAL QUOTIENTS OF DEGREE 1. 2016. ⟨hal-01260587⟩