On the zeros of regular polynomial of a quaternionic variable

Abstract

In this paper, we present some outcomes concerning the zero distributions
of regular polynomials of a quaternionic variable. By invoking
maximum modulus theorem and zero sets of a regular product established
in the recently developed theory of regular functions and polynomials
of a quaternionic variable, we nd new bounds of Enestrom-
Kakeya type for these polynomials with restricted coecients. Additionally,
our ndings extend some classical results from the complex
domain to the realm of quaternionic variables.