Localization of zeros of polar polynomials on the unit disc

TL;DR

This paper establishes a ring-shaped region on the unit circle that contains all zeros of polar polynomials, providing a new geometric insight into their zero distribution.

Contribution

It introduces a novel zero localization result for polar polynomials on the unit circle, including explicit regions containing all zeros.

Findings

Zeros of polar polynomials are contained within a specific ring region on the unit circle.

The paper provides examples illustrating the zero localization result.

Abstract

We derive a useful result about the zeros of the $k$-polar polynomials on the unit circle; in particular we obtain a ring shaped region containing all the zeros of these polynomials. Some examples are presented.