English

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 bb-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}
}