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 zerosof the random trigonometric polynomial T=Tn( Φ, ω )=a bKknKKcos1In the interval (Φ’ , Φ’’ ). Assuming that ak(ω ) are independent randomvariables 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ppn(1 ) 2 log2 32 1212  Outside an exceptional set of measure at most (2/ n ) where  222'(log )4 2 1 2 3SS np pn   β = constant S ~ 1 S’ ~ 11991 Mathematics subject classification (amer. Math. Soc.): 60 B 99