[On the complexity of algebraic numbers]
Let b⩾2 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.
Pour tout entier b supérieur ou égal à 2, nous prouvons la transcendance des nombres réels dont le développement b-adique vérifie une condition combinatoire donnée. Nous en déduisons que le développement b-adique d'un nombre algébrique irrationnel ne peut être engendré par un automate fini.
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Boris Adamczewski 1; Yann Bugeaud 2; Florian Luca 3
@article{CRMATH_2004__339_1_11_0, author = {Boris Adamczewski and Yann Bugeaud and Florian Luca}, title = {Sur la complexit\'e des nombres alg\'ebriques}, journal = {Comptes Rendus. Math\'ematique}, pages = {11--14}, publisher = {Elsevier}, volume = {339}, number = {1}, year = {2004}, doi = {10.1016/j.crma.2004.04.012}, language = {fr}, }
Boris Adamczewski; Yann Bugeaud; Florian Luca. Sur la complexité des nombres algébriques. Comptes Rendus. Mathématique, Volume 339 (2004) no. 1, pp. 11-14. doi : 10.1016/j.crma.2004.04.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.04.012/
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