Generalized Thue-Morse Continued Fractions
Gerardo Gonz\'alez Robert

TL;DR
This paper generalizes the Thue-Morse sequence to TM_m sequences, explores their continued fractions, and extends transcendence results, showing that some existing theorems do not apply in this broader context.
Contribution
It introduces a new generalization of Thue-Morse sequences and extends known transcendence results to these sequences, highlighting limitations of existing theorems.
Findings
Generalization of Thue-Morse sequences to TM_m sequences
Extension of Queffélec's theorem to TM_m continued fractions
Demonstration that Adamczewski and Bugeaud's theorem does not apply here
Abstract
The Thue-Morse sequence is generalized to the sequences and two equivalent definitions are given. This generalization leads to transcendental numbers and has Queff\'elec's theorem on Thue-Morse continued fractions as a special case. It is also shown that the theorem of Adamczewski and Bugeaud for palindromic continued fractions cannot be applied in this case.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Mathematical and Theoretical Analysis · semigroups and automata theory
