The sum-product estimate for large subsets of prime fields
| dc.creator | Garaev, M. Z. | |
| dc.date | 2007-06-05 | |
| dc.date.accessioned | 2026-07-07T08:04:13Z | |
| dc.date.available | 2026-07-07T08:04:13Z | |
| dc.description | Let $\mathbb{F}_p$ be the field of a prime order $p.$ It is known that for any integer $N\in [1,p]$ one can construct a subset $A\subset\mathbb{F}_p$ with $|A|= N$ such that $$ \max\{|A+A|, |AA|\}\ll p^{1/2}|A|^{1/2}. $$ In the present paper we prove that if $A\subset \mathbb{F}_p$ with $|A|>p^{2/3},$ then $$ \max\{|A+A|, |AA|\}\gg p^{1/2}|A|^{1/2}. $$ | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/0706.0702 | |
| dc.identifier | http://arxiv.org/abs/0706.0702 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129870 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11B75, 11T23 | |
| dc.title | The sum-product estimate for large subsets of prime fields | |
| dc.type | text |