On the Number of Rational Points of Jacobians over Finite Fields

Philippe Lebacque (1) , Alexey Zykin (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 ISCP - Interdisciplinary Scientific Center Poncelet

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.

Mots clés: class number; jacobians over finite fields; explicit formulae

Domaines: Théorie des nombres [math.NT]; Géométrie algébrique [math.AG]

Philippe Lebacque, Alexey Zykin. On the Number of Rational Points of Jacobians over Finite Fields. 2014. ⟨hal-01081468⟩