For the Artin-Schreier curve y − y = f(x) defined over a finite field Fq of q elements, the celebrated Weil bound for the number of Fqr -rational points can be sharp, especially in supersingular 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 `-adic monodromy calculations. Roughly spea...
