English

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}
}
R2 v1 2026-06-22T03:16:46.202Z