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 $p^{1∕2+o\left(1\right)}$. 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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Mathematical Subject Classification 2010

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