On the Number of Rational Points of Jacobians over Finite Fields
Number Theory
2014-12-09 v1 Algebraic Geometry
Abstract
In this article we prove lower and upper bounds for class numbers of algebraic curves defined over finite fields. These bounds turn out to be better than most of the previously known bounds obtained using combinatorics. The methods used in the proof are essentially those from the explicit asymptotic theory of global fields. We thus provide a concrete application of effective results from the asymptotic theory of global fields and their zeta-functions.
Cite
@article{arxiv.1412.2609,
title = {On the Number of Rational Points of Jacobians over Finite Fields},
author = {Philippe Lebacque and Alexey Zykin},
journal= {arXiv preprint arXiv:1412.2609},
year = {2014}
}