On the number of rational points of Jacobians over finite fields
Volume 169 / 2015
Acta Arithmetica 169 (2015), 373-384
MSC: Primary 11R29; Secondary 11R58.
DOI: 10.4064/aa169-4-5
Abstract
We prove lower and upper bounds for the 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.
