paper

A Liouville-Type Inequality for Values of Mahler M-Functions

arXiv:2604.08208

Abstract

We establish a Liouville-type inequality for the values, at a common nonzero algebraic point, of arbitrary Mahler Mq-functions. As an application, we prove that no such value is a Liouville number, or even a U -number. This solves a long-standing problem in the field.

A Liouville-Type Inequality for Values of Mahler M-Functions · wovepaper