An explicit sum-product estimate in $\mathbb{F}_p$
| dc.creator | Garaev, M. Z. | |
| dc.date | 2007-02-26 | |
| dc.date.accessioned | 2026-07-07T07:48:51Z | |
| dc.date.available | 2026-07-07T07:48:51Z | |
| dc.description | Let $\mathbb{F}_p$ be the field of residue classes modulo a prime number $p$ and let $A$ be a non-empty subset of $\mathbb{F}_p.$ In this paper we give an explicit version of the sum-product estimate of Bourgain, Katz, Tao and Bourgain, Glibichuk, Konyagin on the size of $\max\{|A+A|, |AA|\}.$ In particular, our result implies that if $1<|A|\le p^{7/13}(\log p)^{-4/13},$ then $$ \max\{|A+A|, |AA|\}\gg \frac{|A|^{15/14}}{(\log|A|)^{2/7}} . $$ | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0702780 | |
| dc.identifier | http://arxiv.org/abs/math/0702780 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124641 | |
| dc.subject | Number Theory | |
| dc.subject | 11B75; 11T23 | |
| dc.title | An explicit sum-product estimate in $\mathbb{F}_p$ | |
| dc.type | text |