Computing Zeta Functions of Nondegenerate Curves
| dc.creator | Castryck, Wouter | |
| dc.creator | Denef, Jan | |
| dc.creator | Vercauteren, Frederik | |
| dc.date | 2006-07-13 | |
| dc.date | 2007-01-08 | |
| dc.date.accessioned | 2026-07-07T07:38:48Z | |
| dc.date.available | 2026-07-07T07:38:48Z | |
| dc.description | In this paper we present a p-adic algorithm to compute the zeta function of a nondegenerate curve over a finite field using Monsky-Washnitzer cohomology. The paper vastly generalizes previous work since all known cases, e.g. hyperelliptic, superelliptic and C_{ab} curves, can be transformed to fit the nondegenerate case. For curves with a fixed Newton polytope, the property of being nondegenerate is generic, so that the algorithm works for almost all curves with given Newton polytope. For a genus g curve over F_{p^n}, the expected running time is O(n^3g^6 + n^2g^{6.5}), whereas the space complexity amounts to O(n^3g^4), assuming p is fixed. | |
| dc.description | 41 pages | |
| dc.identifier | https://arxiv.org/abs/math/0607308 | |
| dc.identifier | http://arxiv.org/abs/math/0607308 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121227 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Computing Zeta Functions of Nondegenerate Curves | |
| dc.type | text |