Point counting in families of hyperelliptic curves in characteristic 2
| dc.creator | Hubrechts, Hendrik | |
| dc.date | 2006-07-14 | |
| dc.date.accessioned | 2026-07-07T07:18:22Z | |
| dc.date.available | 2026-07-07T07:18:22Z | |
| dc.description | Let E_G be a family of hyperelliptic curves over F2^(alg cl) with general Weierstrass equation given over a very small field F. We describe in this paper an algorithm to compute the zeta function of E_g for g in a degree n extension field of F, which has as time complexity O(n^3) and memory requirements O(n^2). With a slightly different algorithm we can get time O(n^2,667) and memory O(n^2,5), and the computation of O(n) curves of the family can be done in time and space O(n^3). All these algorithms are polynomial in the genus. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0607346 | |
| dc.identifier | http://arxiv.org/abs/math/0607346 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114276 | |
| 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 in characteristic 2 | |
| dc.type | text |