QQ客服 官方微博 反馈留言

	A criterion for elliptic curves with second lowest 2-power in L(1)
	Zhao, CL
	2001
英文摘要	Let D = p(1)... p(m), where p(1),.... p(m) are distinct rational primes = 1(mod 8), and m is any positive integer. In this paper, we give a simple combinatorial criterion for the value of the Hecke L-function of the congruent elliptic curve E-D2 : y(2) = x(3) - D-2 x at s = 1, divided by the period omega defined below, to be exactly divisible by 4(m). As a corollary, we obtain a series of non-congruent numbers whose number of prime factors tends to infinity, and for which the corresponding elliptic curves have non-trivial 2-part of Tate-Shafarevich group, which greatly generalizes a result of Razar [8]. Our result is in accord with the predictions of the conjecture of Birch and Swinnerton-Dyer.; Mathematics; SCI(E); 6; ARTICLE; 385-404; 131
语种	英语
出处	SCI
出版者	mathematical proceedings of the cambridge philosophical society
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157326]
专题	数学科学学院
推荐引用方式 GB/T 7714	Zhao, CL. A criterion for elliptic curves with second lowest 2-power in L(1). 2001-01-01.

个性服务

查看访问统计

相关权益政策

暂无数据

收藏/分享

除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。