Skip to main content
eScholarship
Open Access Publications from the University of California

Improvements of the Weil bound for Artin-Schreier curves

  • Author(s): Rojas-León, A
  • Wan, D
  • et al.
Abstract

For the Artin-Schreier curve yq- y = f(x) defined over a finite field Fqof q elements, the celebrated Weil bound for the number of Fqr-rational points can be sharp, especially in super-singular cases and when r is divisible. In this paper, we show how the Weil bound can be significantly improved, using ideas from moment L-functions and Katz's work on ℓ-adic monodromy calculations. Roughly speaking, we show that in favorable cases (which happens quite often), one can remove an extra √q factor in the error term. © 2010 The Author(s).

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.

Main Content
Current View