Constraints on the angular distribution of the zeros of a polynomial of low complexity (Q1173756)

Let \(P(z)\) be a polynomial with complex coefficients of degree \(n\). It is shown that there exists a constant \(C\) such that if \(P\) has at most \(k\) terms then the number of zeros of \(P\) in any open sector of aperture \(\pi/n\) at the origin is at most \(C^{k^ 2}\). This constant is independent of the degree and the coefficients of \(P\).