摘要
设E是Q上带复乘K的椭圆曲线,p是一个奇素数使得E在p处有潜在好通常约化.本文证明,若L(s,E)在s=1处有单零点,则E的p-部分Birch-Swinnerton-Dyer猜想成立.进一步地,本文给出一族椭圆曲线,其导子可以被任意数目的素数整除,具有秩1且满足完整的Birch-Swinnerton-Dyer猜想.
Let E be an elliptic curve over Q with complex multiplication by K and p be an odd prime such that E has potentially good reduction at p.In this paper,we prove that if L(s,E)has a simple zero at s=1,then the p-part of the Birch-Swinnerton-Dyer conjecture of E holds.Moreover,we give a family of elliptic curves with rank one whose conductors can be divided by any number of primes,satisfying the full Birch-Swinnerton-Dyer conjecture.
作者
李永雄
刘余
田野
Yongxiong Li;Yu Liu;Ye Tian
出处
《中国科学：数学》
CSCD
北大核心
2024年第9期1283-1296,共14页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:12288201和11531008)资助项目。
