In 1906, Clark defined and studied the set of p-adic Liouville numbers and, in 1985, Schikhof also studied this set in his book Ultrametric Calculus. In this paper, we introduce the set of weak p-adic Liouville numbers, which is a set of transcendental p-adic numbers that contains the p-adic Liouville numbers, and we show some properties about these numbers. In particular, we shall prove an analogous result to a classic theorem of Maillet about Liouville numbers.

中文翻译：

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p-Adic 刘维尔数的算术性质的一些结果

1906 年，Clark 定义并研究了 p-adic Liouville 数集，1985 年，Schikhof 在他的著作 Ultrametric Calculus 中也研究了这个集。在本文中，我们介绍了弱 p-adic Liouville 数集，它是一组包含 p-adic Liouville 数的超越 p-adic 数，并展示了这些数的一些性质。特别地，我们将证明一个类似于关于刘维尔数的 Maillet 经典定理的类似结果。