On the Arithmetic Behavior of Liouville Numbers under Rational Maps
Number Theory
2019-11-01 v1
Abstract
In 1972, Alnia\c{c}ik proved that every strong Liouville number is mapped into the set of -numbers, for any non-constant rational function with coefficients belonging to an -degree number field. In this paper, we generalize this result by providing a larger class of Liouville numbers (which, in particular, contains the strong Liouville numbers) with this same property (this set is sharp is a certain sense).
Cite
@article{arxiv.1910.14190,
title = {On the Arithmetic Behavior of Liouville Numbers under Rational Maps},
author = {Ana Paula Chaves and Diego Marques and Pavel Trojovsk\' y},
journal= {arXiv preprint arXiv:1910.14190},
year = {2019}
}