Computable Absolutely Pisot Normal Numbers

TL;DR

This paper investigates the convergence rate of an algorithm generating absolutely normal numbers and introduces a new concept of absolute normality using Pisot numbers as non-integer bases.

Contribution

It extends the concept of absolute normality to Pisot bases, providing a framework for expansions with non-integer bases and analyzing their convergence properties.

Findings

Convergence order of the digit-generating algorithm analyzed

Introduction of absolute normality with Pisot bases

Expansion methods for non-integer bases developed

Abstract

We analyze the convergence order of an algorithm producing the digits of an absolutely normal number. Furthermore, we introduce a stronger concept of absolute normality by allowing Pisot numbers as bases, which leads to expansions with non-integer bases.