On the Enestrom-Kakeya Theorem for polynomials of an octonionic variable

TL;DR

This paper extends the Enestrom-Kakeya Theorem to octonionic polynomials, analyzing the location of zeros for polynomials with monotonic coefficients in octonion space.

Contribution

It generalizes a classical polynomial zero theorem to octonions, providing new insights into zero localization for octonionic polynomials with monotonic coefficients.

Findings

Zeros are contained within the closed sphere for polynomials with nonnegative, monotonic coefficients.

Results for polynomials with monotonic coefficient moduli and real parts.

Extension of classical polynomial zero bounds to octonionic setting.

Abstract

To study the zeros of octonionic polynomials, we generalize the well-known Enestrom-Kakeya Theorem to the case of octonions. In this paper, we first deal with octonionic polynomials with nonnegative and monotonic coefficients, and prove that its zero set is contained within the closed sphere of octonion space. Then, we also consider the octonionic polynomials which the coefficients muduli is monotonic and the real parts of the coefficients is monotonic respectively, and get some results.