Growth of polynomials with zeros outside a circle

Abstract

Let P(z) be a polynomial of degree n having all its zeros in \z\ > k > 1. ' (R + *)" + (l + Rk)n Theorem 1 is a generalization of Theorem A in a compact form but unfortunately with the exception of n = 1, (4) does not appear to be sharp for k > 1.However, a precise estimate is given by the following theorem.