On the coefficients of a polynomial with restricted zeros

Abstract

Let

$$ P(z) = a_n z^n + a_n - 1z^{n - 1} + \cdots + a_0 $$

be a complex polynomial of degree n. There is a close connection between the coefficients and the zeros of P(z). In this paper we prove some sharp inequalities concerning the coefficients of the polynomial P(z) with restricted zeros. We also establish a sufficient condition for the separation of zeros of P(z).