On the Transcendence of Power Towers of Liouville Numbers

TL;DR

This paper identifies a dense set of Liouville numbers whose power towers are proven to be transcendental, advancing understanding of the transcendence properties of such numbers.

Contribution

It explicitly constructs a $G_{\delta}$-dense set of Liouville numbers with transcendental power towers, providing new insights into their transcendence behavior.

Findings

A $G_{\delta}$-dense set of Liouville numbers is constructed.

Power towers of these numbers are proven transcendental.

Enhances understanding of transcendence in relation to Liouville numbers.

Abstract

In this paper, among other things, we explicit a $G_{\delta}$-dense set of Liouville numbers, for which the triple power tower of any of its elements is a transcendental number.