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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-4-5,
author = {Philippe Lebacque and Alexey Zykin},
title = {On the number of rational points of Jacobians over finite fields},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {373-384},
zbl = {06456778},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-4-5}
}
Philippe Lebacque; Alexey Zykin. On the number of rational points of Jacobians over finite fields. Acta Arithmetica, Tome 168 (2015) pp. 373-384. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-4-5/