A refinement of Cauchys theorem on the zeros of quaternion polynomial

TL;DR

This paper refines Cauchy's classical theorem on the zeros of quaternionic polynomials and derives zero-free regions for such polynomials with quaternionic coefficients.

Contribution

It provides a significant refinement of Cauchy's theorem specific to quaternion polynomials and applies it to identify zero-free regions.

Findings

Refined bounds on the moduli of quaternion polynomial zeros

Zero-free regions for quaternionic polynomials established

Enhanced understanding of quaternion polynomial zero distribution

Abstract

In this paper, we shall present an interesting and significant refinement of a classical result of Cauchy about the moduli of the zeros of a quaternionic polynomial. As an application of this result we shall obtain zero-free regions of polynomials having quaternionic coefficients.