On the Sum-Product Problem on Elliptic Curves

Details On the Sum-Product Problem on Elliptic Curves On the Sum-Product Problem on Elliptic Curves

2008-06-03

arxiv.org/abs/0806.0640v1

Mathematics

Number Theory

13 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On the Sum-Product Problem on Elliptic Curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Sum-Product Problem on Elliptic Curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Sum-Product Problem on Elliptic Curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-153768