On complex positive definite functions on Z_n vanishing on squares

Details On complex positive definite functions on Z_n vanishing on squares On complex positive definite functions on Z_n vanishing on squares

2008-11-09

arxiv.org/abs/0811.1360v3

Mathematics

Number Theory

The paper has been completely revised and posted in a new form and with a new title, as accepted for publishing

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On complex positive definite functions on Z_n vanishing on squares does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On complex positive definite functions on Z_n vanishing on squares, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On complex positive definite functions on Z_n vanishing on squares will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-484124