The Irrationality Exponents of Computable Numbers
Number Theory
2014-10-07 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1410.1017,
title = {The Irrationality Exponents of Computable Numbers},
author = {Verónica Becher and Yann Bugeaud and Theodore A. Slaman},
journal= {arXiv preprint arXiv:1410.1017},
year = {2014}
}