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

By Boris Adamczewski, Yann Bugeaud. 2005

223 citations recorded by the source corpus.

Let b ≥ 2 be an integer. We prove that the b-ary 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.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/55805270410243ff0f5ca66f5baabeffce93e9a5

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In Computational Theory and Mathematics

1. Boris Adamczewski
2. Yann Bugeaud
3. Nimish A. Shah

In Mathematical Physics

1. Boris Adamczewski
2. Yann Bugeaud
3. Michel Waldschmidt
4. Samir Siksek
5. Julien Cassaigne

Citations in the corpus

• Dynamics for β-shifts and Diophantine approximation (2007, methodology): “Theorem ABL was extended in [2] in the following way.”