Abstract
In 1972, Alniacik proved that every strong Liouville number is mapped into the set of $$U_m$$ -numbers, for any non-constant rational function with coefficients belonging to an m-degree number field. In this paper, we generalize this result by providing a larger class of Liouville numbers (which, in particular, contains the strong Liouville numbers) with this same property (this set is sharp is a certain sense).
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