On the upper 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. **44** (1974), 446-448

MSC:
Primary 60G55; Secondary 92A10

DOI:
https://doi.org/10.1090/S0002-9939-1974-0438473-5

MathSciNet review:
0438473

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Abstract: Let be the number of real roots of where 's are independent random variables identically distributed with a common characteristic function is a positive constant, are nonzero real numbers such that . Then

(i) ;

(ii) ;

(iii) .

**[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**, https://doi.org/10.1093/qmath/21.3.309**[2]**G. Samal and M. N. Mishra,*On the upper bound of the number of real roots of a random algebraic equation with infinite variance*, J. London Math. Soc. (2)**6**(1973), 598–604. MR**0438472**, https://doi.org/10.1112/jlms/s2-6.4.598**[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. III*, Proc. Amer. Math. Soc.**39**(1973), 184–189. MR**0315786**, https://doi.org/10.1090/S0002-9939-1973-0315786-8

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1974-0438473-5

Keywords:
Random variables,
infinite variance,
real roots,
random algebraic equations

Article copyright:
© Copyright 1974
American Mathematical Society