Sur la complexité des nombres algébriques

Abstract : Let bgreater-or-equal, slanted2 be an integer. We prove that real numbers whose b-ary expansion satisfies some given, simple, combinatorial condition are transcendental. This implies that the b-ary expansion of any algebraic irrational number cannot be generated by a finite automaton.
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https://hal.archives-ouvertes.fr/hal-00085619
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Submitted on : Thursday, July 13, 2006 - 11:11:52 AM
Last modification on : Tuesday, April 24, 2018 - 1:34:12 PM

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Boris Adamczewski, Yann Bugeaud, Florian Luca. Sur la complexité des nombres algébriques. Comptes Rendus Mathématique, Elsevier Masson, 2004, 339, num. 1, pp.11-14. ⟨10.1016/j.crma.2004.04.012⟩. ⟨hal-00085619⟩

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