Pisot Numbers and Primes

TL;DR

This paper explores the relationship between Pisot numbers and prime numbers through a novel transform, providing formulas to identify non-integer power Pisot limit points on the semi-line.

Contribution

It introduces a new transform linking Pisot numbers and primes and offers formulas to locate specific Pisot limit points, advancing understanding of their distribution.

Findings

Derived three formulas for Pisot limit points.

Identified all non-integer power Pisot limit points on the semi-line.

Established relations between Pisot numbers and primes.

Abstract

We define and study a transform whose iterates bring to the fore interesting relations between Pisot numbers and primes. Although the relations we describe are general, they take a particular form in the Pisot limit points. We give three elegant formulae, which permit to locate on the whole semi-line all limit points that are not integer powers of other Pisot numbers.