On the Distribution of Complex Roots of Random Polynomials with Heavy-tailed Coefficients

Friedrich Götze, Dmitry Zaporozhets

Consider a random polynomial $G_n(z)={\xi }_n{z}^n+...+{\xi }_{1}z+{\xi }_0$ with i.i.d. complex-valued coefficients. Suppose that the distribution of $\log (1+\log (1+|{\xi }_0|))$ has a slowly varying tai…