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.

引用

页码：21 / 40

页数：20

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