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

Authors:
G. Samal and M. N. Mishra

Journal:
Proc. Amer. Math. Soc. **36** (1972), 557-563

MSC:
Primary 60G99

DOI:
https://doi.org/10.1090/S0002-9939-1972-0315785-5

MathSciNet review:
0315785

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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 's are independent random variables with a common characteristic function

*C*, a positive constant. Then for ,

**[1]**E. A. Evans,*On the number of real roots of a random algebraic equation*, Proc. London Math. Soc. (3)**15**(1965), 731–749. MR**0180997**, https://doi.org/10.1112/plms/s3-15.1.731**[2]**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****[3]**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.**[4]**G. Samal,*On the number of real roots of a random algebraic equation*, Proc. Cambridge Philos. Soc.**58**(1962), 433–442. MR**0139221****[5]**G. Samal and M. N. Mishra,*On the lower bound of the number of real roots of a random algebraic equation with infinite variance*, Proc. Amer. Math. Soc.**33**(1972), 523–528. MR**0295411**, https://doi.org/10.1090/S0002-9939-1972-0295411-4

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0315785-5

Keywords:
Random equation,
infinite variance,
real zeros,
lower bound

Article copyright:
© Copyright 1972
American Mathematical Society