The Irrationality Exponents of Computable Numbers

We prove that a real number a greater than or equal to 2 is the irrationality exponent of some computable real number if and only if a is the upper limit of a computable sequence of rational numbers. Thus, there are computable real numbers whose irrationality exponent is not computable.

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Bibliographic Details
Main Authors Becher, Verónica, Bugeaud, Yann, Slaman, Theodore A
Format Journal Article
LanguageEnglish
Published 03.10.2014
Subjects
Mathematics - Number Theory
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Summary:We prove that a real number a greater than or equal to 2 is the irrationality exponent of some computable real number if and only if a is the upper limit of a computable sequence of rational numbers. Thus, there are computable real numbers whose irrationality exponent is not computable.
DOI:10.48550/arxiv.1410.1017