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arXiv · 1806.02262

Computing Zeta Functions of Cyclic Covers in Large Characteristic

Vishal Arul·Alex J. Best·Edgar Costa·Richard Magner·Nicholas Triantafillou
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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.

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Vishal Arul, Alex J. Best, Edgar Costa, Richard Magner, Nicholas Triantafillou. 2018-11-12. Computing Zeta Functions of Cyclic Covers in Large Characteristic. https://doi.org/10.2140/obs.2019.2.37

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