New asymptotics for the mean number of zeros of random trigonometric polynomials with strongly dependent Gaussian coefficients

Thibault Pautrel

We consider random trigonometric polynomials of the form \[ f_n(t):=\frac{1}{\sqrt{n}} \sum_{k=1}^{n}a_k \cos(k t)+b_k \sin(k t), \] where $(a_k{)}_{k\ge 1}$ and $(b_k{)}_{k\ge 1}$ a…