On the complexity of algebraic number I. Expansions in integer bases
Number Theory
2012-05-07 v1
Abstract
Let be an integer. We prove that the -adic expansion of every irrational algebraic number cannot have low complexity. Furthermore, we establish that irrational morphic numbers are transcendental, for a wide class of morphisms. In particular, irrational automatic numbers are transcendental. Our main tool is a new, combinatorial transcendence criterion.
Keywords
Cite
@article{arxiv.math/0511674,
title = {On the complexity of algebraic number I. Expansions in integer bases},
author = {Boris Adamczewski and Yann Bugeaud},
journal= {arXiv preprint arXiv:math/0511674},
year = {2012}
}