A bootstrap for the number of $\mathbb{F}_{q^r}$-rational points on a curve over $\mathbb{F}_q$
Algebraic Geometry
2017-04-18 v1
Abstract
In this note we present a fast algorithm that finds for any the number of rational points on a smooth absolutely irreducible curve defined over assuming that we know , where is the genus of . The proof of its validity is given in detail and its working are illustrated with several examples. In an Appendix we list the Python function in which we have implemented the algorithm together with other routines used in the examples.
Cite
@article{arxiv.1704.04661,
title = {A bootstrap for the number of $\mathbb{F}_{q^r}$-rational points on a curve over $\mathbb{F}_q$},
author = {Santiago Molina and Narcís Sayols and Sebastià Xambó-Descamps},
journal= {arXiv preprint arXiv:1704.04661},
year = {2017}
}