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

1973 ◽  
Vol 39 (1) ◽  
pp. 184-184 ◽  
Author(s):  
G. Samal ◽  
M. N. Mishra
Keyword(s):  
Lower Bound ◽  
Algebraic Equation ◽  
Infinite Variance ◽  
Real Roots ◽  
Number Of Real Roots

scholarly journals On the Lower Bound for the Number of Real Roots of a Random Algebraic Equation

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Takashi Uno
Keyword(s):  
Lower Bound ◽  
Algebraic Equation ◽  
Random Variables ◽  
Real Roots ◽  
Number Of Real Roots

We estimate a lower bound for the number of real roots of a random alegebraic equation whose random coeffcients are dependent normal random variables.

scholarly journals Lower bound for the number of real roots of a random algebraic polynomial

1983 ◽  
Vol 35 (1) ◽  
pp. 18-27 ◽  
Author(s):  
M. N. Mishra ◽  
N. N. Nayak ◽  
S. Pattanayak
Keyword(s):  
Lower Bound ◽  
Algebraic Polynomial ◽  
Random Variables ◽  
Domain Of Attraction ◽  
Independent Random Variables ◽  
Real Numbers ◽  
Exceptional Set ◽  
Real Roots ◽  
Normal Law ◽  
Number Of Real Roots

AbstractLet X1, X2, …, Xn be identically distributed independent random variables belonging to the domain of attraction of the normal law, have zero means and Pr{Xr ≠ 0} > 0. Suppose a0, a1, …, an are non-zero real numbers and max and εn is such that as n → ∞, εn. If Nn be the number of real roots of the equation then for n > n0, Nn > εn log n outside an exceptional set of measure at most provided limn→∞ (kn/tn) is finite.

On the number of real roots of a random algebraic equation. II

1939 ◽  
Vol 35 (2) ◽  
pp. 133-148 ◽  
Author(s):  
J. E. Littlewood ◽  
A. C. Offord
Keyword(s):  
Algebraic Equation ◽  
Present Series ◽  
Interested Reader ◽  
Real Roots ◽  
Number Of Real Roots

An equation with real coefficients and given degree n being selected at random, about how many real roots may it be expected to have? The present series of papers is concerned with this question and matters arising out of it. The results we have arrived at were stated without proof in our paper I (with the same general title), which contains also some introductory remarks to which we may refer the interested reader. Here we summarize as follows.

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