On the lower bound of the number of real roots of a random algebraic equation with infinite variance

Authors:
G. Samal and M. N. Mishra

Journal:
Proc. Amer. Math. Soc. **33** (1972), 523-528

MSC:
Primary 60E05

DOI:
https://doi.org/10.1090/S0002-9939-1972-0295411-4

MathSciNet review:
0295411

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the number of real roots of a random algebraic equation , where the coefficients 's are independent random variables with common characteristic function , *C* being a positive constant and . It is proved that

*n*tends to infinity.

**[1]**B. V. Gnedenko and A. N. Kolmogorov,*Limit distributions for sums of independent random variables*, Addison-Wesley Publishing Company, Inc., Cambridge, Mass., 1954. Translated and annotated by K. L. Chung. With an Appendix by J. L. Doob. MR**0062975****[2]**J. E. Littlewood and A. C. Offord,*On the number of real roots of a random algebraic equation*. II, Proc. Cambridge Philos. Soc.**35**(1939), 133-148.**[3]**G. Samal,*On the number of real roots of a random algebraic equation*, Proc. Cambridge Philos. Soc.**58**(1962), 433–442. MR**0139221**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0295411-4

Keywords:
Random variables,
stable distribution,
infinite variance,
random algebraic equations

Article copyright:
© Copyright 1972
American Mathematical Society