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Computing zeta functions
of cyclic covers in large characteristic
Vishal Arul, Alex J. Best, Edgar Costa, Richard Magner and Nicholas Triantafillou |
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Vol. 2 (2019), No. 1, 37–53
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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 . 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. |
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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Authors |
| Vishal Arul | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
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| Alex J. Best | |
| Department of Mathematics Boston University Boston, MA United States |
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| Edgar Costa | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
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| Richard Magner | |
| Department of Mathematics Boston University Boston, MA United States |
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| Nicholas Triantafillou | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
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