On the variance of the number of real roots of a random trigonometric polynomial

[摘要] This paper provides an upper estimate for the variance of the number of real zeros of the random trigonometric polynomialg1cosθ+g2cos2θ+…+gncosnθ. The coefficientsgi(i=1,2,…,n)are assumed independent and normally distributed with mean zero and variance one.

[学科分类] 应用数学