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

Authors:
G. Samal and M. N. Mishra

Journal:
Proc. Amer. Math. Soc. **39** (1973), 184-189

MSC:
Primary 60G99

MathSciNet review:
0315786

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Abstract: Let be the number of real roots of a random algebraic equation , where 's are independent random variables with common characteristic function being a positive constant, and are nonzero real numbers. Let . If , then

It may be remarked that the coefficients 's in the above equation are not identically distributed.

**[1]**J. E. A. Dunnage,*The number of real zeros of a class of random algebraic polynomials. II*, Quart. J. Math. Oxford Ser. (2)**21**(1970), 309–319. MR**0275485****[2]**G. Samal,*On the number of real roots of a random algebraic equation*, Proc. Cambridge Philos. Soc.**58**(1962), 433–442. MR**0139221****[3]**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**, 10.1090/S0002-9939-1972-0295411-4**[4]**G. Samal and M. N. Mishra,*On the lower bound of the number of real roots of a random algebraic equation with infinite variance. II*, Proc. Amer. Math. Soc.**36**(1972), 557–563. MR**0315785**, 10.1090/S0002-9939-1972-0315785-5

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DOI:
https://doi.org/10.1090/S0002-9939-1973-0315786-8

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

Article copyright:
© Copyright 1973
American Mathematical Society