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

Boris Adamczewski; Colin Faverjon

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

Number Theory 2026-04-10 v1

Authors: Boris Adamczewski , Colin Faverjon

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.

Keywords

Mahler M-functions Liouville-type inequality Algebraic numbers Diophantine approximation

Cite

@article{arxiv.2604.08208,
  title  = {A Liouville-Type Inequality for Values of Mahler M-Functions},
  author = {Boris Adamczewski and Colin Faverjon},
  journal= {arXiv preprint arXiv:2604.08208},
  year   = {2026}
}