On the complexity of algebraic number I. Expansions in integer bases

Details On the complexity of algebraic number I. Expansions in integer bases On the complexity of algebraic number I. Expansions in integer bases

2005-11-28

arxiv.org/abs/math/0511674v1

Mathematics

Number Theory

Scientific paper

Let $b \ge 2$ be an integer. We prove that the $b$-adic expansion of every
irrational algebraic number cannot have low complexity. Furthermore, we
establish that irrational morphic numbers are transcendental, for a wide class
of morphisms. In particular, irrational automatic numbers are transcendental.
Our main tool is a new, combinatorial transcendence criterion.

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