Potential energy of totally positive algebraic integers

Abstract

Given positive real numbers, we prove two inequalities involving their potential energy and their power sums. We also prove a general inequality involving the energy and the discriminant.

This can be applied to the case of totally positive irreducible polynomials, although in that more specialised setting the results are weaker than those obtained by Smyth's method.

Keywords

• Potential
• energy
• totally
• positive
• algebraic
• integers