Department of Mathematics, College of Judea and Samaria, 44837 Ariel, Israel
Kenneth J. Hochberg ; Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel
Abstract:
We derive several new results on the asymptotic behavior of the roots of random polynomial equations, including conditions under which the distributions of the zeros of certain random polynomials tend to the uniform distribution on the circumference of a circle centered at the origin. We also derive a probabilistic analog of the Cauchy-Hadamand theorem that enables us to obtain the radius of convergence of a random power series.