Three Dimensional Corners: A Box Norm Proof
| dc.creator | Lacey, Michael T. | |
| dc.creator | McClain, William | |
| dc.date | 2008-04-18 | |
| dc.date.accessioned | 2026-07-07T09:33:28Z | |
| dc.date.available | 2026-07-07T09:33:28Z | |
| dc.description | 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. | |
| dc.description | 86 pages | |
| dc.identifier | https://arxiv.org/abs/0804.3019 | |
| dc.identifier | http://arxiv.org/abs/0804.3019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159142 | |
| dc.subject | Number Theory | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Combinatorics | |
| dc.title | Three Dimensional Corners: A Box Norm Proof | |
| dc.type | text |