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On the algebraicity of Thue-Morse and period-doubling continued fractions (2005.11937v2)
Published 25 May 2020 in math.NT and math.CO
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.