The Thue-Morse continued fractions in characteristic $2$ are algebraic

Yann Bugeaud, Guo-Niu Han

Let $a,b$ be distinct, non-constant polynomials in ${\mathbb{F}}_2[z]$. Let ${\xi }_{a,b}$ be the power series in ${\mathbb{F}}_2((z^{-1}))$ whose sequence of partial quotients is the…