The maximum or minimum number of rational points on curves of genus three over finite fields

Details The maximum or minimum number of rational points on curves of genus three over finite fields The maximum or minimum number of rational points on curves of genus three over finite fields

2001-04-07

arxiv.org/abs/math/0104086v1

Compositio Mathematica 134 (p. 87-111) 2002

Mathematics

Algebraic Geometry

28 pages including the appendix. Main paper by Kristin Lauter, appendix by Jean-Pierre Serre

Scientific paper

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. For some q, we also obtain improvements on the
upper bound for the number of rational points on a genus 3 curve over F_q.

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