Title: Point counting in families of hyperelliptic curves
Authors: Hubrechts, Hendrik # ×
Issue Date: Feb-2008
Publisher: Springer-Verlag New York
Series Title: Foundations of Computational Mathematics vol:8 issue:1 pages:137-169
Abstract: Let E_Gamma be a family of hyperelliptic curves defined by Y^2 = Q(X,Gamma) where Q is defined over a small finite field of odd characteristic. Then with gamma in an extension degree n field over this small field, we present a deterministic algorithm for computing the zeta function of the curve E_gamma 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.
ISSN: 1615-3375
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
× corresponding author
# (joint) last author

Files in This Item:

There are no files associated with this item.

Request a copy


All items in Lirias are protected by copyright, with all rights reserved.

© Web of science