The Maximum or Minimum Number of Rational Points on Genus Three Curves over Finite Fields

Kristin Lauter; Jean-Pierre Serre

doi:10.1023/A:1020246226326

Abstract

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We show that for all finite fields Fq, there exists a curve C over Fq 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 Fq.

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Article contents

The Maximum or Minimum Number of Rational Points on Genus Three Curves over Finite Fields

Abstract

Keywords

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

The Maximum or Minimum Number of Rational Points on Genus Three Curves over Finite Fields

Abstract

Keywords

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