What question did this study set out to answer?

The aim is to extend and refine results related to the zeros of quaternionic polynomials under certain coefficient constraints.

April 20, 2026

On the Zeros of Quaternionic Polynomials with Restricted Coefficient

Key Points

The aim is to extend and refine results related to the zeros of quaternionic polynomials under certain coefficient constraints.
Analyzed quaternionic polynomials with non-negative coefficients.
Refined previous work by Carney et al. on zeros of quaternionic polynomials.
Used mathematical proofs to establish the generalization.
Demonstrated that the zeros of the general quaternionic polynomials also lie within a specific boundary.
Provided a stronger understanding of the behavior of these polynomials.
Clarified the implications for the coefficients structure on the zeros.

Abstract

Let P (z) =₉=₀^na₉z^j be a polynomial of degree n such that a₍ a₍-₁. . . a₁ a₀ 0. Then according to Eneström–Kakeya theorem all the zeros of P (z) lie in |z| 1. This important result was recently extended to quaternionic setting by Carney, Gardner, Keaton, and Powers. In this paper, we shall generalize and refine the results of Carney, Gardner, Keaton, Powers, and Tripathi.

On the Zeros of Quaternionic Polynomials with Restricted Coefficient

Key Points

Abstract

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