Computing Zeta Functions of Cyclic Covers in Large Characteristic

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 Gonc{c}alvesu0027s generalization of Kedlayau0027s algorithm for cyclic covers, and Harveyu0027s work on Kedlayau0027s algorithm for large characteristic.