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2019•P-Adic Numbers Ultrametric Analysis and ApplicationsRequires access

Some Results on Arithmetic Properties of p-Adic Liouville Numbers

Jean Lelis, Diego Marques

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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.

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What this paper is about

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.

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Available 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.

Key concepts: Ultrametric space, Mathematics, Transcendental number, Set (abstract data type), Real number, Transcendental function, Discrete mathematics, Pure mathematics

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