Growth of Polynomials Having All Zeros on the Disk

Let p(z)=a_nz^n+∑i = v ^n a_n-i^ z^n-i, 1≤ v n, be a polynomial of degree n having all zeros on |z|=k, k≤ 1. In this paper we measure the growth of p(z) by estimating {max_|z|=R|p(z)|}{\max_|z|=1|p(z)|}^s from above for any R≥ 1 and arbitrary positive integer s.