The maximum or minimum number of rational points on curves of genus three over finite fields
Algebraic Geometry
2007-05-23 v1 Number Theory
Abstract
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.
Cite
@article{arxiv.math/0104086,
title = {The maximum or minimum number of rational points on curves of genus three over finite fields},
author = {Kristin Lauter and Jean-Pierre Serre},
journal= {arXiv preprint arXiv:math/0104086},
year = {2007}
}
Comments
28 pages including the appendix. Main paper by Kristin Lauter, appendix by Jean-Pierre Serre