Sum-product estimates via directed expanders
| dc.creator | Vu, Van | |
| dc.date | 2007-05-04 | |
| dc.date.accessioned | 2026-07-07T07:59:40Z | |
| dc.date.available | 2026-07-07T07:59:40Z | |
| dc.description | Let $\F_q$ be a finite field of order $q$ and $P$ be a polynomial in $\F_q[x_1, x_2]$. For a set $A \subset \F_q$, define $P(A):=\{P(x_1, x_2) | x_i \in A \}$. Using certain constructions of expanders, we characterize all polynomials $P$ for which the following holds \vskip2mm \centerline{\it If $|A+A|$ is small, then $|P(A)|$ is large.} \vskip2mm The case $P=x_1x_2$ corresponds to the well-known sum-product problem. | |
| dc.identifier | https://arxiv.org/abs/0705.0715 | |
| dc.identifier | http://arxiv.org/abs/0705.0715 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128455 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.title | Sum-product estimates via directed expanders | |
| dc.type | text |