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Nombres réels de complexité sous-linéaire : mesures d'irrationalité et de transcendance

  • Boris Adamczewski EMAIL logo and Yann Bugeaud

Abstract

By means of a quantitative version of the Schmidt Subspace Theorem, we obtain irrationality and trancendence measures for real numbers whose expansion in an integer base has a sublinear complexity. We further give several applications of our general results to Sturmian, automatic, and morphic numbers, and to lacunary series. In particular, we extend a theorem on Sturmian numbers established by Bundschuh in 1980. We also provide a first step towards a conjecture of Becker by proving that irrational automatic real numbers are either S- or T-numbers. This improves upon a recent result of Adamczewski and Cassaigne, who established that irrational automatic real numbers cannot be Liouville numbers.

Received: 2008-11-14
Revised: 2010-03-15
Published Online: 2011-03-23
Published in Print: 2011-September

© Walter de Gruyter Berlin · New York 2011

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