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On the Number of Real Roots of a Random Algebraic Equation

Published online by Cambridge University Press:  24 October 2008

G. Samal
G. Samal
Affiliation:
Department of MathematicsBirkbeck CollegeLondon
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Abstract

Let Nn be the number of real roots of a random algebraic equation The coefficients ξν are independent random variables identically distributed with expectation zero; the variance and third absolute moment are finite and non-zero. It is proved that

where εν tends to zero, but εν log n tends to infinity. The measure of the exceptional set tends to zero as n tends to infinity.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 3 , July 1962 , pp. 433 - 442
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

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