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

Adamczewski, Boris; Bugeaud, Yann

doi:10.4007/annals.2007.165.547

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

Published in Annals of Mathematics • Mar 1, 2007

Authors:

Boris Adamczewski

Yann Bugeaud

Abstract

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...

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Subject

Irrational number

Mathematics

Transcendental number

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