  We prove that the upper bound for the van der Corput property of the set of
perfect squares is O((log n)^{-1/3}), giving an answer to a problem considered
by Ruzsa and Montgomery. We do it by constructing non-negative valued, normed
trigonometric polynomials with spectrum in the set of perfect squares not
exceeding n, and a small free coefficient a_0=O((log n)^{-1/3}).
