Some Results on Arithmetic Properties of p-Adic Liouville Numbers

Abstract

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.