Let E(C q) be the set of C q-rational points on an elliptic curve E over a finite field C q of q elements given by an affine Weierstraß equation. We use x(P) to denote the x-component of a point P = (x(P), y(P)), ⋯ E and for an integer n consider character sums S n(a, b) = ∑ Ψ (ax(P) + bx(nP)) , a, b ⋯ C q, P⋯E(C q) with an additive character Ψ of C q. In the case when gcd (n, #E(C q)) is sufficiently large, we obtain a new bound for such sums. In particular, we show that for any positive integer n ⌊ # E(F q), we have S n(a, b) = O(q 9/ 10uniformly over n, a ⋯ C* q and b ⋯ C q.
|Number of pages||4|
|Journal||Boletin de la Sociedad Matematica Mexicana|
|Publication status||Published - Apr 2009|
- Character sums
- Elliptic curves