Rank Statistics for a Family of Elliptic Curves over a Function Field

被引：0
|
作者：
Pomerance, Carl [1 ]
Shparlinski, Igor E. [2 ]
机构：
[1] Dartmouth Coll, Dept Math, Hanover, NH 03755 USA
[2] Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
来源：
PURE AND APPLIED MATHEMATICS QUARTERLY | 2010年 / 6卷 / 01期
关键词：
rank of elliptic curve; function field; multiplicative order; ARTINS CONJECTURE; PSEUDOPRIMES;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that the average and typical ranks in a certain parametric family of elliptic curves described by D. Ulmer tend to infinity as the parameter d ->infinity. This is perhaps unexpected since by a result of A. Brumer, the average rank for all elliptic curves over a function field of positive characteristic is asymptotically bounded above by 2.3.
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页码：21 / 40
页数：20
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