Abstract

Let P be a complex polynomial of degree n with P(0)=1 and Cauchy radius 1 about the origin. We discuss the order of magnitude of the minimal number N=N(ϵn,n) such that min1≤k≤N|P(e2πik/N)|≤1−ϵn. Previous estimates of N=O(n3/2) are improved to N=O(nlogn). Some other related properties of these polynomials are also exhibited.