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arXiv · 1910.14190

On the Arithmetic Behavior of Liouville Numbers under Rational Maps

Ana Paula Chaves·Diego Marques·Pavel Trojovsk\' y
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Abstract

In 1972, Alniaçik 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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Ana Paula Chaves, Diego Marques, Pavel Trojovsk\' y. 2019-10-31. On the Arithmetic Behavior of Liouville Numbers under Rational Maps. https://arxiv.org/abs/1910.14190

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