Families of Newton-like inequalities for sets of self-conjugate complex numbers

TL;DR

This paper introduces new families of Newton-like inequalities for elementary symmetric functions of self-conjugate complex numbers in the right half-plane, independent of their proximity to the real axis.

Contribution

It presents the first known inequalities of this type that do not depend on how close the complex numbers are to the real axis.

Findings

Derived families of inequalities for self-conjugate complex numbers

Inequalities are independent of proximity to the real axis

First known inequalities of this kind for such sets

Abstract

We derive families of Newton-like inequalities involving the elementary symmetric functions of sets of self-conjugate complex numbers in the right half-plane. These are the first known inequalities of this type which are independent of the proximity of the complex numbers to the real axis.