Computing Zeta Functions of Cyclic Covers in Large Characteristic
arXiv:1806.02262 · doi:10.2140/obs.2019.2.37
Abstract
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.
16 pages; v2 with minor changes