Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-26T07:36:34.988Z Has data issue: false hasContentIssue false
  • English
  • Français

On the 3-part of the Birch and Swinnerton-Dyer conjecture

Published online by Cambridge University Press:  01 July 1997

SHAOWEI ZHANG
SHAOWEI ZHANG
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, P.R. China
Get access Rights & Permissions [Opens in a new window]

Abstract

Let K=ℚ(√−3). Assume E is an elliptic curve defined over K, with complex multiplication by OK, the ring of integers of K. Ω∈[Copf]X is a minimal period of E. For each prime v of K, let cv denote the Tamagawa number [E(Kv)[ratio ]E0(Kv)]. Let L(E/K, s) denote the Hasse–Weil L-function of E/K. [lfloor][mid ][rfloor](E/K)=ker{H1(K, E)→[oplus ]vH1(Kv, E)} denotes the Tate-Shafarevic group of E/K.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 1 , July 1997 , pp. 1 - 8
Copyright
Cambridge Philosophical Society 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)