Thirteenth Algorithmic Number Theory Symposium ANTS-XIII University of Wisconsin, Madison July 16 – 20, 2018 Thirteenth Algorithmic Number Theory Symposium (ANTS-XIII) July 16 – 20, 2018

Computing zeta functions of cyclic covers in large characteristic

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

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 eectiveness 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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