On continued fractions of quadratic formal series over \({\mathbb F}_q (X)\) (Q2717599)

The author is interested in stating, for the case of formal Laurent series over a finite field, characterizations of purely periodic or palindromic continued fraction expansions, as well as in obtaining estimates for the length of the period of quadratic continued fractions. We quote here one of the results in this paper: NEWLINENEWLINENEWLINELet \(f= \sum_{j=s}^\infty f_jX^{-j}\in \mathbb{F}_q ((X^{-1}))\), with \(s\leq 0\) and \(f_s\neq 0\), be a Laurent series quadratic over \(\mathbb{F}_q(X)\). Then, the continued fraction expansion of \(f\) is purely periodic if and only if \(f\) satisfies an equation \(A_2f^2+ A_1f+ A_0=0\) with \(A_i\in \mathbb{F}_q(X)\) and with \(\deg A_0<\deg A_1\) and \(\deg A_2<\deg A_1\).