The analysis establishes that values of Mahler M-functions are not Liouville numbers in algebraic settings, solving a key problem.
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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Adamczewski et al. (2026) studied this question.
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