  We generalize the Sarkozy-Furstenberg theorem on squares in difference sets
of integers, and show that, given any positive definite function f:Z_N->C with
density at least r(N), where r(N)=O((\log N)^{-c}), there is a perfect square
s<=N/2 such that f(s) is non-zero. We do not rely on the usual analysis of the
dichotomy of randomness and periodicity of a set and iterative application of
the Hardy-Littlewood method. Instead, we find a bound for the van der Corput
property of the set of squares.
