Counting points on curves using a map to P^1
Number Theory
2014-09-11 v2 Algebraic Geometry
Abstract
We introduce a new algorithm to compute the zeta function of a curve over a finite field. This method extends Kedlaya's algorithm to a very general class of curves using a map to the projective line. We develop all the necessary bounds, analyse the complexity of the algorithm and provide some examples computed with our implementation.
Keywords
Cite
@article{arxiv.1402.6758,
title = {Counting points on curves using a map to P^1},
author = {Jan Tuitman},
journal= {arXiv preprint arXiv:1402.6758},
year = {2014}
}