On the Sum-Product Problem on Elliptic Curves
| dc.creator | Ahmadi, Omran | |
| dc.creator | Shparlinski, Igor | |
| dc.date | 2008-06-03 | |
| dc.date.accessioned | 2026-07-07T09:42:36Z | |
| dc.date.available | 2026-07-07T09:42:36Z | |
| dc.description | Let $\E$ be an ordinary elliptic curve over a finite field $\F_{q}$ of $q$ elements and $x(Q)$ denote the $x$-coordinate of a point $Q = (x(Q),y(Q))$ on $\E$. Given an $\F_q$-rational point $P$ of order $T$, we show that for any subsets $\cA, \cB$ of the unit group of the residue ring modulo $T$, at least one of the sets $$ \{x(aP) + x(bP) : a \in \cA, b \in \cB\} \quad\text{and}\quad \{x(abP) : a \in \cA, b \in \cB\} $$ is large. This question is motivated by a series of recent results on the sum-product problem over finite fields and other algebraic structures. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/0806.0640 | |
| dc.identifier | http://arxiv.org/abs/0806.0640 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162241 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11G05, 11L07, 11T23 | |
| dc.title | On the Sum-Product Problem on Elliptic Curves | |
| dc.type | text |