J Austral Math Soc Ser A 49 pp149--160, 1990.

On the Average Number of Real Zeros of a Class of Random Algebraic Equations

N. N. Nayak and S. Bagh

Abstract

Let g₁, g₂, ..., g_n be a sequence of nutually independent, normally distributed, random variables with mathematical expectation zero and variance unity. In this work, we obtain the average number of real zeros of the random algebraic equations åⁿ_k=1k^s g_k(w)t^k = C, where C is a constant independent of t and not necessarily zero. This average is (1/p)(1 + Ö(2s+ 1))log n, when n is large and s is non-negative.

1980 AMS Subject Classification (1985 Revision): 05A17, 05A19

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Authors

N. N. Nayak

Orissa University of Agriculture and Technology, Bhubaneswae, 751003, Orissa, India.

S. Bagh

Department of Statistics, Sambalput University, Jyoti Vihar, 768019, Orissa, India.