On the algebraicity of Thue-Morse and period-doubling continued fractions

2020/05/25 by Hu, Yining, Wei-Han, Guoniu
#05A15 #11B50 #11J70 #11T55 #11Y65 #1B85 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2005.11937

Abstract

We put forward several general conjectures concerning the algebraicity or transcendence of continued fractions and Stieltjes continued fractions defined by the Thue-Morse and period-doubling sequences in characteristic 2. We present our Guess'n'Prove method, in which we exploit the structure of automata, for proving some of our conjectures in special cases.

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