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A Hyperelliptic Smoothness Test, II |
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| Authors: | Lenstra, H. W., Jr Pila, J. Pomerance, Carl |
| Affiliation: | Department of Mathematics #3840 University of California Berkeley CA 94720–3840 USA hwl{at}math.berkeley.edu and Mathematisch Instituut, Universiteit Leiden Postbus 9512 2300 RA Leiden The Netherlands hwl{at}math.leidenuniv.nl Department of Mathematics, University of Melbourne Parkville 3052, Australia pila{at}ms.unimelb.edu.au Mail address: 6 Goldthorns Avenue, Kew 3101 Australia Bell Laboratories — Lucent Technologies 600 Mountain Avenue, Murray Hill, NJ 07974 USA carlp{at}research.bell-labs.com |
| Abstract: | This series of papers presents and rigorously analyzes a probabilisticalgorithm for finding small prime factors of an integer. Thealgorithm uses the Jacobian varieties of curves of genus 2 inthe same way that the elliptic curve method uses elliptic curves.This second paper in the series is concerned with the orderof the group of rational points on the Jacobian of a curve ofgenus 2 defined over a finite field. We prove a result on thedistribution of these orders. 2000 Mathematical Subject Classification:11Y05, 11G10, 11M20, 11N25. |
| Keywords: | smooth integer hyperelliptic curve abelian surface |
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