ON A RESULT CONCERNING REAL ZEROS OF A RANDOM TRIGONOMETRIC POLYNOMIAL - MISHRA, DR. P. K.; DHAL, DIPTY RANI (IJRDO -JOURNAL OF MATHEMATICS, 2016)
Let EN( T; Φ’ , Φ’’ ) denote the average number of real roots of the random trigonometric polynomial T=Tn( θ, ω )= a  k n K K cos 1  In the interval (Φ’ , Φ’’ ). Clearly , T can have at most 2n zeros in the interval ( 0, 2π ) .Assuming that ak(ω )s to be mutually independent identically distributed normal random variables , Dunnage has shown that in the interval 0 ≤ θ ≤ 2π all save a certain exceptional set of the functions (Tn ( θω )) have          13 3 13 11 log 3 2 O n n n zeros when n is large. We consider the same family of trigonometric polynomials and use the Kac_rice formula for the expectation of the number of real roots and obtain that EN ( T ; 0 , 2π ) (log ) 6 2 O n n  This result is better than that of Dunnage since our constant is (1/√2) Times his constant and our error term is smaller . the proof is based on the convergence of an integral of which an asymptotic estimation is obtained . 1991 Mathematics subject classification (amer. Math. Soc.): 60 B 99.