On the Number of Rational Points of Jacobians over Finite Fields

2014/12/08 by Philippe Lebacque, Lebacque, Philippe, Zykin, Alexey
Computer Science · #Algebraic Geometry (math.AG) #Coding theory and cryptography #Cryptographic Implementations and Security #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1412.2609

openalex publication_date 2014/12/08 · openalex created_date 2022/09/18 · openalex updated_date 2026/07/28

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.

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