On the number of real roots of a random algebraic equation

Abstract

Let Nn(w) be the number of real roots of the random algebraic equation [formula omitted], where the ξv{w)'s are independent, identically distributed random variables belonging to the domain of attraction of the normal law with mean zero and [formula omitted]; also the av's are nonzero real numbers such that [formula omitted] where [formula omitted] and [formula omitted]. It is shown that for any sequence of positive constants (εn, n ≥ 0) satisfying εn → 0 and [formula omitted] there is a positive constant μ so that [formula omitted] for all n0 sufficiently large. © 1993, Australian Mathematical Society. All rights reserved.