It is well known that the expected number of real zeros of a random cosine polynomial , , with the being standard Gaussian i.i.d. random variables, is asymptotically . On the other hand, some of the previous works on the random cosine polynomials with dependent coefficients show that such polynomials have at least expected real zeros lying in one period. We investigate two classes of random cosine polynomials with pairwise equal blocks of coefficients. First, we prove that a random cosine polynomial with the blocks of coefficients being of a fixed length and satisfying possesses the same expected real zeros as the classical case. Afterwards, we study a case containing only two equal blocks of coefficients, and show that in this case significantly more real zeros should be expected compared with those of the classical case.
"Real zeros of random trigonometric polynomials with pairwise equal blocks of coefficients." Rocky Mountain J. Math. 50 (4) 1451 - 1471, August 2020. https://doi.org/10.1216/rmj.2020.50.1451