Weierstrass Points and Curves Over Finite Fields
Karl-Otto Stöhr, José Felipe Voloch · Proceedings of the London Mathematical Society · 1986
For any projective embedding of a non-singular irreducible complete algebraic curve defined over a finite field, we obtain an upper bound for the number of its rational points. The constants in the bound are related to the Weierstrass order-sequence associated with the projective embedding. The bounds obtained lead to a proof of the Riemann hypothesis for curves over finite fields and yield several improvements on it.