On the location of zeros of a quaternion polynomial

TL;DR

This paper develops new bounds for locating zeros of quaternion polynomials, generalizing existing results by applying the maximum modulus theorem to improve understanding of their distribution.

Contribution

It introduces novel Cauchy bounds for quaternion polynomial zeros, extending previous findings and enhancing methods for zero localization in quaternionic analysis.

Findings

Derived new Cauchy bounds for quaternion polynomial zeros

Generalized recent results on zero distribution

Applied maximum modulus theorem to quaternion polynomials

Abstract

In this paper, we are concerned with the problem of locating the zeros of polynomials of a quaternionic variable with quaternionic coefficients. We derive some new Cauchy bounds for the zeros of a polynomial by virtue of maximum modulus theorem. Our results will generalise some recently proved results about the distribution of zeros of a quaternionic polynomial.