On the location of zeros of a polynomial (Q2919573)

Let \(f(z):=z^n+\sum_{j=0}^{n-1}a_j z^j\). A classical result of Cauchy states that all the zeros of the polynomial \(f\) lie in \(| z| <1+A\), where \(A=\max\{| a_0| ,\dots,| a_{n-1}|\}\). But this estimate does not reflect the fact that as \(A\to 0\), all the zeros approach the origin, \(z=0\). In the paper under review, the author generalizes an improved bound obtained by \textit{F. G. Boese} and \textit{W. J. Luther} [IEEE Trans. Autom. Control 34, No. 9, 998--1001 (1989; Zbl 0693.93064)]. In addition, the author establishes a zero free region around the origin for an \(n^{\text{th}}\) degree polynomial.