Roots of random polynomials with arbitrary coefficients

Yen Do, Oanh Nguyen, Van Vu

Published 2015-07-17Version 1

In this paper, we prove optimal local universality for roots of random polynomials with arbitrary coefficients of polynomial growth. As an application, we derive, for the first time, sharp estimates for the number of real roots of these polynomials, even when the coefficients are not explicit. Our results also hold for series; in particular, we prove local universality for random hyperbolic series.