On continued fraction expansions of quadratic irrationals in positive characteristic

Frédéric Paulin (1) , Uri Shapira (2)

1 Topologie, géométrie, dynamique
2 TECHNION - Department of Mathematics

Let $P$ be a prime polynomial in the variable $Y$ over a finite field and let $f$ be a quadratic irrational in the field of formal Laurant series in the variable $Y^{-1}$. We study the asymptotic properties of the degrees of the coefficients of the continued fraction expansion of quadratic irrationals such as $P^nf$ and prove results that are in sharp contrast to the analogue situation in zero characteristic.

Domaines: Systèmes dynamiques [math.DS]; Théorie des nombres [math.NT]

Frédéric Paulin, Uri Shapira. On continued fraction expansions of quadratic irrationals in positive characteristic. 2018. ⟨hal-01698250⟩