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On Mahler $U$-numbers under rational maps
In 1906, Maillet proved that every nonconstant rational function over $\mathbb{Q}$ maps Liouville numbers to Liouville numbers. Let $R$ be a nonconstant rational function with real algebraic coefficients, of degree $d$, and let $e$ be the degree of its minimal field of definition over $\mathbb{Q}$.
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