On the number of real roots of a random algebraic equation

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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.

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Pratihari, D., Panda, R. K., & Pattanaik, B. P. (1993). On the number of real roots of a random algebraic equation. Journal of the Australian Mathematical Society, 54(1), 86–96. https://doi.org/10.1017/S1446788700037009

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