ON CURVES OVER FINITE FIELDS WITH JACOBIANS OF SMALL EXPONENT

被引：2

作者：

Ford, Kevin ^{[1
]}

Shparlinski, Igor ^{[2
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[2] Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2008年 / 4卷 / 05期

关键词：

Jacobian; group structure; distribution of divisors;

D O I：

10.1142/S1793042108001687

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that finite fields over which there is a curve of a given genus g >= 1 with its Jacobian having a small exponent, are very rare. This extends a recent result of Duke in the case of g = 1. We also show that when g = 1 or g = 2, our lower bounds on the exponent, valid for almost all finite fields F-q and all curves over F-q, are best possible.

引用

页码：819 / 826

页数：8

共 17 条

[1]

[Anonymous], 1995, ARITHMETIC ELLIPTIC

[2]

Avanzi R., 2005, ELLIPTIC HYPERELLIPT

[3] Almost all reductions modulo p of an elliptic curve have a large exponent [J].