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Abstract
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We describe an algorithm to compute the zeta function of a cyclic
cover of the projective line over a finite field of characteristic
that runs
in time
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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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Keywords
computational number theory, superelliptic, hyperelliptic,
arithmetic geometry, Monsky–Washnitzer cohomology, zeta
functions, p-adic
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Mathematical Subject Classification 2010
Primary: 11G20
Secondary: 11M38, 11Y16, 14G10
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Milestones
Received: 2 March 2018
Revised: 17 September 2018
Accepted: 18 September 2018
Published: 13 February 2019
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