Diophantine properties of real numbers generated by finite automata
Number Theory
2012-05-07 v1
Abstract
We study some diophantine properties of automatic real numbers and we present a method to derive irrationality measures for such numbers. As a consequence, we prove that the -adic expansion of a Liouville number cannot be generated by a finite automaton, a conjecture due to Shallit.
Keywords
Cite
@article{arxiv.math/0601604,
title = {Diophantine properties of real numbers generated by finite automata},
author = {Boris Adamczewski and Julien Cassaigne},
journal= {arXiv preprint arXiv:math/0601604},
year = {2012}
}