Some special character sums over elliptic curves

Shparlinski Igor*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)37-40
Number of pages4
JournalBoletin de la Sociedad Matematica Mexicana
Volume15
Issue number1
Publication statusPublished - Apr 2009

Keywords

  • Character sums
  • Elliptic curves

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