Complex Zeros of Trigonometric Polynomials with Standard Normal Random Coefficients - Farahmand, K.; Grigorash, A. (Journal of mathematical analysis and applications, 2001)
In this paper, we obtain an exact formula for the average density of the distribution of complex zeros of a random trigonometric polynomial η0+η1cosθ+η2cos2θ+⋯+ηncosnθ in (0,2π), where the coefficients ηj=aj+ιbj, and ajj=1n and bjj=1n are sequences of independent normally distributed random variables with mean 0 and variance 1. We also provide the limiting behaviour of the zeros density function as n tends to infinity. The corresponding results for the case of random algebraic polynomials are known.