On distribution of zeros of random polynomials in complex plane

Ildar Ibragimov, Dmitry Zaporozhets

Let $G_n(z)={\xi }_0+{\xi }_{1}z+...+{\xi }_n{z}^n$ be a random polynomial with i.i.d. coefficients (real or complex). We show that the arguments of the roots of $G_n(z)$ are uniformly distributed i…