English

Computing Zeta Functions of Cyclic Covers in Large Characteristic

Number Theory 2019-02-13 v2 Algebraic Geometry

Abstract

We describe an algorithm to compute the zeta function of a cyclic cover of the projective line over a finite field of characteristic pp that runs in time p1/2+o(1)p^{1/2 + o(1)}. We confirm its practicality and effectiveness by reporting on the performance of our SageMath implementation on a range of examples. The algorithm relies on Gon\c{c}alves's generalization of Kedlaya's algorithm for cyclic covers, and Harvey's work on Kedlaya's algorithm for large characteristic.

Keywords

Cite

@article{arxiv.1806.02262,
  title  = {Computing Zeta Functions of Cyclic Covers in Large Characteristic},
  author = {Vishal Arul and Alex J. Best and Edgar Costa and Richard Magner and Nicholas Triantafillou},
  journal= {arXiv preprint arXiv:1806.02262},
  year   = {2019}
}

Comments

16 pages; v2 with minor changes

R2 v1 2026-06-23T02:21:17.451Z