Point counting in families of hyperelliptic curves in characteristic 2

dc.creatorHubrechts, Hendrik
dc.date2006-07-14
dc.date.accessioned2026-07-07T07:18:22Z
dc.date.available2026-07-07T07:18:22Z
dc.descriptionLet 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.description23 pages
dc.identifierhttps://arxiv.org/abs/math/0607346
dc.identifierhttp://arxiv.org/abs/math/0607346
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114276
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject14Q05, 11G20 (Primary) 12H25, 14F30, 14G50 (Secondary)
dc.titlePoint counting in families of hyperelliptic curves in characteristic 2
dc.typetext

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