On the zeros of a quaternionic polynomial with restricted coefficients

Abstract

In this paper, we are concerned with the problem of locating the zeros of regular polynomials of a quaternionic variable with restricted quaternionic coefficients. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets established in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results generalize some recently proved results about the distribution of zeros of a quaternionic polynomial.