The Thue-Morse continued fractions in characteristic 2 are algebraic

2022/03/04 by Bugeaud, Yann, Han, Guo-Niu
#11A55 #11J61 #11J70 #11T55 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2203.02213

Abstract

Let a, b be distinct, non-constant polynomials in \mathbb F₂ [z]. Let ξ_{a, b} be the power series in \mathbb F₂((z^-1)) whose sequence of partial quotients is the Thue-Morse sequence over \a, b\. We establish that ξ_a,b is algebraic of degree 4.

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