The Thue–Morse continued fractions in characteristic 2 are algebraic
Volume 214 / 2024
Acta Arithmetica 214 (2024), 1-22
MSC: Primary 11J70; Secondary 11A55, 11B85, 11J61, 11T55.
DOI: 10.4064/aa221212-5-1
Published online: 1 March 2023
Abstract
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 Thue–Morse sequence over $\{a, b\}$. We establish that $\xi_{a,b}$ is algebraic of degree $4$.
