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arXiv · 2005.11937

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

Yining Hu·Guoniu Wei-Han
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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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Yining Hu, Guoniu Wei-Han. 2020-05-25. On the algebraicity of Thue-Morse and period-doubling continued fractions. https://arxiv.org/abs/2005.11937

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