华东师范大学学报(自然科学版) ›› 2007, Vol. 2007 ›› Issue (5): 12-19.

• 数学 统计学 • 上一篇    下一篇

椭圆曲线L(1)的 3-adic 赋值达到下界的判别

孙乃喆   

  1. 天津科技大学 数学系, 天津 300457
  • 收稿日期:2006-11-01 修回日期:2007-02-26 出版日期:2007-09-25 发布日期:2007-09-25
  • 通讯作者: 孙乃喆

Criterion for Elliptic Curves with the Lowest 3-Power in L(1)(Chinese)

SUN Nai-zhe   

  1. Department of Mathematics, Tianjin University of Science and Technology, Tianjin 300457, China
  • Received:2006-11-01 Revised:2007-02-26 Online:2007-09-25 Published:2007-09-25
  • Contact: SUN Nai-zhe

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摘要： 设 K 为三次分圆域,
E D[[lambda]] :y2=x3-24 3 3 D[lambda]为定义在 K 上的椭圆曲线, 其中 D 为 K 中无平方因子的代数整数, [lambda]属于Z . 邱德荣用一个非常复杂的函数给出了当 [lambda]=2,4 时E D[lambda] 的 Hecke L- 函数在点 1 处的值(除以椭圆周期) 恰被 3 n/2 -1 整除 的充要条件. 本文用加权图的语言给出了这个充要条件一个简单的组合论的刻画.

关键词: 椭圆曲线, 复乘, Hecke L-函数, 加权图, 生成树, 椭圆曲线, 复乘, Hecke L-函数, 加权图, 生成树

Abstract: Let K be the 3rd cyclotomic field, E D[lambda] :y2=x3-24 3 3 D[lambda]] be an elliptic curve defined over K, where D\in K is a square-free algebraic integer and [[lambda]] in Z . Qiu Derong found a rather complicated function as the criterion for the value of the Hecke L-function attached to the curve E D[lambda]([lambda]=2,4) at s=1 divided by the period [OMEGA] to be exactly divisible by 3 n/2 -1 . This paper reduced Qiu’s criterion to a simpler version in terms of weighted graphs.

Key words: complex multiplication, Hecke L-function, weighted graph, spanning tree, elliptic curves, complex multiplication, Hecke L-function, weighted graph, spanning tree

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