A sum-product estimate in finite fields, and applications
| dc.creator | Bourgain, Jean | |
| dc.creator | Katz, Nets | |
| dc.creator | Tao, Terence | |
| dc.date | 2003-01-29 | |
| dc.date | 2006-03-10 | |
| dc.date.accessioned | 2026-07-07T06:35:35Z | |
| dc.date.available | 2026-07-07T06:35:35Z | |
| dc.description | Let $A$ be a subset of a finite field $F := \Z/q\Z$ for some prime $q$. If $|F|^δ< |A| < |F|^{1-δ}$ for some $δ> 0$, then we prove the estimate $|A+A| + |A.A| \geq c(δ) |A|^{1+\eps}$ for some $\eps = \eps(δ) > 0$. This is a finite field analogue of a result of Erdos and Szemeredi. We then use this estimate to prove a Szemeredi-Trotter type theorem in finite fields, and obtain a new estimate for the Erdos distance problem in finite fields, as well as the three-dimensional Kakeya problem in finite fields. | |
| dc.description | 29 pages. The distance set result needs to be restricted to the case when -1 is not a square | |
| dc.identifier | https://arxiv.org/abs/math/0301343 | |
| dc.identifier | http://arxiv.org/abs/math/0301343 | |
| dc.identifier | Geom. Func. Anal. 14 (2004), 27-57 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99835 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05B25, 11T99 | |
| dc.title | A sum-product estimate in finite fields, and applications | |
| dc.type | text |