Three Dimensional Corners: A Box Norm Proof

Details Three Dimensional Corners: A Box Norm Proof Three Dimensional Corners: A Box Norm Proof

2008-04-18

arxiv.org/abs/0804.3019v1

Mathematics

Number Theory

86 pages

Scientific paper

In an additive group (G,+), a three-dimensional corner is the four points g, g+d(1,0,0), g+d(0,1,0), g+d(0,0,1), where g is in G^3, and d is a non-zero element of G. The Ramsey number of interest is R_3(G) the maximal cardinality of a subset of G^3 that does not contain a three-dimensional corner. Furstenberg and Katznelson have shown R_3(Z_N) is little-o of N^3, and in fact the corresponding result holds in all dimensions, a result that is a far reaching extension of the Szemeredi Theorem. We give a new proof of the finite field version of this fact, a proof that is a common generalization of the Gowers proof of Szemeredi's Theorem for four term progressions, and the result of Shkredov on two-dimensional corners. The principal tool are the Gowers Box Norms.

Affiliated with

Also associated with

No associations

Rating

Three Dimensional Corners: A Box Norm Proof 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 Three Dimensional Corners: A Box Norm Proof, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Three Dimensional Corners: A Box Norm Proof will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-304146