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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.

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).

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