Abstract
NUMBER OF ZEROS OF A CLASS OF RANDOM ALGEBRAIC POLYNOMIAL
Sima Rout* and P. K. Mishra
ABSTRACT
The expected number of crossings of a Random algebraic polynomial f(n)→∞, crosses the line y= mx, when m is any real value and (m2/n)→0 as n→∞ reduces to only one. We know the expected number of times that a polynomial of degree n with independent normally distributed random real coefficients asymptotically crosses the line y= m x, when m is any real value and (m2/n)→0 as n→∞. Many authors Kac,[4] Farahmad,[3] Nayak.[7] Rice[9] have investigated the plane symmetric solutions of number of crossings of different polynomials and equations in general relativity. Here, we study the expected number of crossings of a Random algebraic polynomial f (n)→∞, crosses the line y= mx, when m is any real value and (m2/n) →0 as n→∞ reduces to only one. This theory agrees with the present observational facts pertaining to general relativity. The present paper shows that the expected number of crossings of a Random algebraic polynomial for m >exp(f(n)), where f is any function of n such that f(n)→∞, this expected number of crossings reduces to only one.
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