Potential energy of totally positive algebraic integers

TL;DR

This paper establishes new inequalities relating potential energy, power sums, and discriminants of totally positive algebraic integers, with implications for their polynomial properties.

Contribution

It introduces novel inequalities connecting potential energy, power sums, and discriminants for totally positive algebraic integers, advancing understanding in algebraic number theory.

Findings

Proved inequalities involving potential energy and power sums.

Derived an inequality linking energy and discriminant.

Applied results to totally positive irreducible polynomials.

Abstract

Given positive real numbers, we prove two inequalities involving their potential energy and their power sums. We also prove an inequality involving the energy and the discriminant and apply it to deduce a result on totally positive irreducible polynomials.