%0 Journal Article
%T On complex positive definite functions on Z_n vanishing on squares
%A Sinisa Slijepcevic
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0811.1360v3