On the Structure of Sets with Few Three-Term Arithmetic Progressions
| dc.creator | Croot, Ernie | |
| dc.date | 2006-07-07 | |
| dc.date.accessioned | 2026-07-07T07:18:10Z | |
| dc.date.available | 2026-07-07T07:18:10Z | |
| dc.description | Fix a density d in (0,1], and let F_p^n be a finite field, where we think of p fixed and n tending to infinity. Let S be any subset of F_p^n having the minimal number of three-term progressions, subject to the constraint |S| is at least dp^n. We show that S must have some structure, and that up to o(p^n) elements, it is a union of a small number of cosets of a subspace of dimension n-o(n). | |
| dc.description | This is a much cleaner version of a proof published on the arxives three years ago, but where this one holds for finite fields F_p^n. The result in this paper is much clearer than that published previously | |
| dc.identifier | https://arxiv.org/abs/math/0607208 | |
| dc.identifier | http://arxiv.org/abs/math/0607208 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114203 | |
| dc.subject | Number Theory | |
| dc.subject | 11P70 | |
| dc.title | On the Structure of Sets with Few Three-Term Arithmetic Progressions | |
| dc.type | text |