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), 446448
MSC:
Primary 60G55; Secondary 92A10
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
(43 #1239)
 [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
(55 #11384a)
 [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
(47 #4335), http://dx.doi.org/10.1090/S00029939197303157868
 [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), 309319. MR 43 #1239. MR 0275485 (43:1239)
 [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. 6 (1973), 598604. MR 0438472 (55:11384a)
 [3]
 , 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), 184189. MR 0315786 (47:4335)
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DOI:
http://dx.doi.org/10.1090/S00029939197404384735
PII:
S 00029939(1974)04384735
Keywords:
Random variables,
infinite variance,
real roots,
random algebraic equations
Article copyright:
© Copyright 1974
American Mathematical Society
