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Diophantine properties of real numbers generated by finite automata

Boris Adamczewski·Julien Cassaigne
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Abstract

We study some diophantine properties of automatic real numbers and we present a method to derive irrationality measures for such numbers. As a consequence, we prove that the $b$-adic expansion of a Liouville number cannot be generated by a finite automaton, a conjecture due to Shallit.

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Boris Adamczewski, Julien Cassaigne. 2006-01-25. Diophantine properties of real numbers generated by finite automata. https://arxiv.org/abs/math/0601604

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