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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
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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

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