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math.AG2001
Geometric methods for improving the upper bounds on the number of rational points on algebraic curves over finite fields
Kristin Lauter, Jean-Pierre Serre
Currently, the best upper bounds on the number of rational points on an absolutely irreducible, smooth, projective algebraic curve of genus g defined over a finite field F_q come e…
math.AG2001
The maximum or minimum number of rational points on curves of genus three over finite fields
Kristin Lauter, Jean-Pierre Serre
We show that for all finite fields F_q, there exists a curve C over F_q of genus 3 such that the number of rational points on C is within 3 of the Serre-Weil upper or lower bound.…