Point counting in families of hyperelliptic curves
| dc.creator | Hubrechts, H. | |
| dc.date | 2006-01-18 | |
| dc.date | 2007-01-29 | |
| dc.date.accessioned | 2026-07-07T07:43:17Z | |
| dc.date.available | 2026-07-07T07:43:17Z | |
| dc.description | Let E_G be a family of hyperelliptic curves defined by Y^2=Q(X,G), where Q is defined over a small finite field of odd characteristic. Then with g in an extension degree n field over this small field, we present a deterministic algorithm for computing the zeta function of the curve E_g by using Dwork deformation in rigid cohomology. The time complexity of the algorithm is O(n^(2.667)) and it needs O(n^(2.5)) bits of memory. A slight adaptation requires only O(n^2) space, but costs time O(n^3). An implementation of this last result turns out to be quite efficient for n big enough. | |
| dc.description | 33 pages. Changes: major revision | |
| dc.identifier | https://arxiv.org/abs/math/0601438 | |
| dc.identifier | http://arxiv.org/abs/math/0601438 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122768 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14Q05, 11G20 (Primary) 12H25, 14F30, 14G50 (Secondary) | |
| dc.title | Point counting in families of hyperelliptic curves | |
| dc.type | text |