Computing zeta functions of cyclic covers in large characteristic
Vishal Arul, Alex J. Best, Edgar Costa, Richard Magner, Nicholas Triantafillou · The Open Book Series · 2019
We describe an algorithm to compute the zeta function of a cyclic cover of the projective line over a finite field of characteristic p that runs in time 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 Gonçalves's generalization of Kedlaya's algorithm for cyclic covers, and Harvey's work on Kedlaya's algorithm for large characteristic.The authors are grateful to the organizers of Sage Days 87, where this project began.We would also like to thank the reviewers for their many helpful comments.