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A Hyperelliptic Smoothness Test, II
Author(s) -
Lenstra H. W.,
Pila J.,
Pomerance Carl
Publication year - 2002
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/84.1.105
Subject(s) - mathematics , jacobian matrix and determinant , elliptic curve , smoothness , genus , schoof's algorithm , prime (order theory) , integer (computer science) , finite field , series (stratigraphy) , order (exchange) , pure mathematics , discrete mathematics , mathematical analysis , quarter period , combinatorics , computer science , paleontology , botany , biology , programming language , finance , economics
This series of papers presents and rigorously analyzes a probabilistic algorithm for finding small prime factors of an integer. The algorithm uses the Jacobian varieties of curves of genus 2 in the same way that the elliptic curve method uses elliptic curves. This second paper in the series is concerned with the order of the group of rational points on the Jacobian of a curve of genus 2 defined over a finite field. We prove a result on the distribution of these orders. 2000 Mathematical Subject Classification : 11Y05, 11G10, 11M20, 11N25.