On the 2-adic valuations of central L-values of elliptic curves

JOURNAL OF NUMBER THEORY

卷:204

Article

Choi, Junhwa¹ 

[1] Korea Inst Adv Study, Sch Math, 85 Hoegi Ro, Seoul 02455, South Korea

关键词: Elliptic curves;    L-values;    Birch and Swinnerton-Dyer conjecture;   

DOI  :  10.1016/j.jnt.2019.04.011

来源: Elsevier

【 摘 要 】

The paper generalizes the method of Zhao for an infinite family of Q-curves and establishes some analytic results on the 2-part of the Birch and Swinnerton-Dyer conjecture. We give lower bounds on the 2-adic valuations of the algebraic part of the L-values at s = 1 for those Q-curves. Moreover, we also discuss 2-descent on Q-curves and compute their Mordell-Weil group and Tate-Shafarevich group. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free