On the Transcendence of Power Towers of Liouville Numbers
In this paper, among other things, we explicit a $G_δ$-dense set of Liouville numbers, for which the triple power tower of any of its elements is a transcendental number.
math.NT↗
arXiv subjects
Pavel Trojovsk\' y
Publications and source records attributed to Pavel Trojovsk\' y.
On the Arithmetic Behavior of Liouville Numbers under Rational Maps
In 1972, Alniaçik proved that every strong Liouville number is mapped into the set of $U_m$-numbers, for any non-constant rational function with coefficients belonging to an $m$-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).
math.NT↗