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The irrationality exponents of computable numbers


Authors: Verónica Becher, Yann Bugeaud and Theodore A. Slaman
Journal: Proc. Amer. Math. Soc. 144 (2016), 1509-1521
MSC (2010): Primary 11J04; Secondary 03Dxx
DOI: https://doi.org/10.1090/proc/12841
Published electronically: October 6, 2015
MathSciNet review: 3451228
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Abstract: We establish that there exist computable real numbers whose irrationality exponent is not computable.


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Verónica Becher
Affiliation: Departamento de Computacion, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, C1428EGA Ciudad Autónoma de Buenos Aires, Argentina
Email: vbecher@dc.uba.ar

Yann Bugeaud
Affiliation: UFR de Mathématique et d’Informatique, Université de Strasbourg, 7 rue René Descartes, 67084 Strasbourg Cedex, France
Email: bugeaud@math.unistra.fr

Theodore A. Slaman
Affiliation: Department of Mathematics, 970 Evans Hall, University of California Berkeley, Berkeley, California 94720
Email: slaman@math.berkeley.edu

DOI: https://doi.org/10.1090/proc/12841
Keywords: Irrationality exponent, computability, Cantor set
Received by editor(s): August 22, 2014
Received by editor(s) in revised form: May 13, 2015
Published electronically: October 6, 2015
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2015 American Mathematical Society