On thep-part of the Birch–Swinnerton-Dyer conjecture for elliptic curves with complex multiplication by the ring of integers of

DOI10.1017/S0305004116000852zbMath1431.11083arXiv1605.08245WikidataQ122923008 ScholiaQ122923008MaRDI QIDQ4600748

Yukako Kezuka

Publication date: 12 January 2018

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.08245

zbMATH Keywords

complex multiplicationBirch-Swinnerton-Dyer conjecture

Mathematics Subject Classification ID

Elliptic curves (14H52) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items (4)

A classical family of elliptic curves having rank one and the \(2\)-primary part of their Tate-Shafarevich group non-trivial ⋮ On the weak forms of the 2-part of Birch and Swinnerton-Dyer conjecture ⋮ Tamagawa number divisibility of central \(L\)-values of twists of the Fermat elliptic curve ⋮ A lower bound result for the central \(L\)-values of elliptic curves

Cites Work

• The ``main conjectures of Iwasawa theory for imaginary quadratic fields
• On the conjecture of Birch and Swinnerton-Dyer
• A criterion for elliptic curves with lowest 2-power in L(1)
• Algorithm for determining the type of a singular fiber in an elliptic pencil
• A criterion for elliptic curves with lowest 2-power in L(1) (II) This work was supported by NSFC and RFDP.
• The diophantine equation X3 + Y3 = DZ3 and the conjectures of Birch and Swinnerton-Dyer.
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