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This is a Quantitative Study study.

October 7, 2025Open Access

On the location of zeros of a quaternion polynomial

Key Points

New bounds for the zeros of quaternion polynomials improve understanding of their distribution.
The research presents additional Cauchy bounds derived from the maximum modulus theorem.
Results enhance existing knowledge about the zeros of polynomials with quaternionic coefficients.
Applications of these findings may extend to complex and quaternionic analysis.

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.

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Cite This Study

Rather et al. (Sat,) studied this question.

synapsesocial.com/papers/68e5a0557f330f793683f183 https://doi.org/https://doi.org/10.48550/arxiv.2502.16295

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