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A HYPERELLIPTIC SMOOTHNESS TEST, II

Published online by Cambridge University Press:  13 February 2002

H. W. LENSTRA ,
J. PILA  and
CARL POMERANCE
H. W. LENSTRA
Affiliation:
Department of Mathematics #3840 University of California, Berkeley CA 94720–3840 USAhwl@math.berkeley.edu and Mathematisch Instituut, Universiteit Leiden Postbus 9512 2300 RA Leiden The Netherlandshwl@math.leidenuniv.nl
J. PILA
Affiliation:
Department of Mathematics, University of Melbourne, Parkville 3052, Australiapila@ms.unimelb.edu.au Mail address: 6 Goldthorns Avenue, Kew 3101 Australia
CARL POMERANCE
Affiliation:
Bell Laboratories — Lucent Technologies, 600 Mountain Avenue, Murray Hill, NJ 07974 USAcarlp@research.bell-labs.com
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Abstract

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.

Keywords

smooth integerhyperelliptic curveabelian surface
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 84 , Issue 1 , March 2002 , pp. 105 - 146
Copyright
2002 London Mathematical Society

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