# β-fraction continue dans le corps des séries formelles sur un corps fini

Mohamed Hbaib
Université de Sfax
https://www.researchgate.net/profile/Mohamed-Hbaib

Date(s) : 20/05/2014   iCal
11 h 00 min - 12 h 00 min

Continued 𝛽-fractions with formal power series over finite fields

Let be a unit Pisot quadratic series over a finite field Fq. We define a β-fraction algorithm, inspired by Euclid’s algorithm. We show that any element of Fq(x;β) has a finite continued β-fraction whenever this expansion does not finish finitely by polynomials of degree 1.