AVERAGE NUMBER OF REAL ZEROS OF 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 zeros of the random trigonometric polynomial T=Tn( Φ, ω )= a bK k n K K cos 1  In the interval (Φ’ , Φ’’ ). Assuming that ak(ω ) are independent random variables identically distributed according to the normal law and that bk = kp (p ≥ 0) are positive constants, we show that EN( T : 0, 2π ) n O n p p n (1 ) 2 log 2 3 2 1 2 1 2                    Outside an exceptional set of measure at most (2/ n ) where    2 2 2 ’(log ) 4 2 1 2 3 SS n p p n      β = constant S 1 S’ 1 1991 Mathematics subject classification (amer. Math. Soc.): 60 B 99