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arXiv · 2604.08208

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

Boris Adamczewski·Colin Faverjon
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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.

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Boris Adamczewski, Colin Faverjon. 2026-04-09. A Liouville-Type Inequality for Values of Mahler M-Functions. https://arxiv.org/abs/2604.08208

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