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).

中文翻译：

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有理映射下刘维尔数的算术行为

1972 年，Alniacik 证明了对于任何系数属于 $m$-度数域的非常数有理函数，每个强刘维尔数都映射到 $U_m$-数集。在本文中，我们通过提供具有相同属性的更大类 Liouville 数（特别是包含强 Liouville 数）来概括这个结果（这个集合在某种意义上是尖锐的）。