ON A QUARTIC EQUATION AND TWO FAMILIES OF HYPERQUADRATIC CONTINUED FRACTIONS IN POWER SERIES FIELDS (modified version)

Kh Ayadi (1) , A Lasjaunias (2)

1 FSS - Faculté des Sciences de Sfax
2 IMB - Institut de Mathématiques de Bordeaux

We discuss the continued fraction expansion, in the field of power series over a finite prime field, of characteristic p>3, of the solution of a particular quartic equation. This allows us to describe two very large families of hyperquadratic continued fractions. Finally, we compute the irrationality measure for the solution of this quartic equation and we obtain two different values according to the remainder of p in the division by 3.

Domaines: Théorie des nombres [math.NT]

Kh Ayadi, A Lasjaunias. ON A QUARTIC EQUATION AND TWO FAMILIES OF HYPERQUADRATIC CONTINUED FRACTIONS IN POWER SERIES FIELDS (modified version). 2016. ⟨hal-01260579⟩