Some genus 3 curves with many points
Roland Auer, Jaap Top
Abstract
Using an explicit family of plane quartic curves, we prove the existence of a genus 3 curve over any finite field of characteristic 3 whose number of rational points stays within a fixed distance from the Hasse-Weil-Serre upper bound. We also provide an intrinsic characterization of so-called Legendre elliptic curves.
Create a lesson
Related papers
An ergodic approach to equations of the form x+y=α(n)
Vitaly Bergelson, Hao Pan, Saúl Rodríguez Martín
Rogers--Ramanujan identities from the geometry of Xa=Yb
Yifeng Huang, Kenny Lau, Ken Ono
Computational results on sums of a prime with squares or cubes
Kenny Applegate, Kyle Pratt
Finding New Limit Points of Mahler Measure by Methods of Missing Data Restoration
Jean-Marc Sac-Épée, Souad El Otmani, Armand Maul et al.
Low moments of automorphic random multiplicative function sums
Sun-Kai Leung
A problem of Yang and Chen on weighted representation functions
Shuang-Shuang Li, Ya-Ting Xu, Xiao-Hui Yan