On the weak forms of the 2-part of Birch and Swinnerton-Dyer conjecture

On the weak forms of the 2-part of Birch and Swinnerton-Dyer conjecture

In this paper, we investigate the weak forms of the 2-part of the conjecture of Birch and Swinnerton-Dyer, and prove a lower bound for the 2-adic valuation of the algebraic part of the central value of the complex L -series for the family of quadratic twists of all optimal elliptic curves over ${\ma...

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Veröffentlicht in:Mathematical proceedings of the Cambridge Philosophical Society 2020-01, Vol.168 (1), p.197-209
1. Verfasser: ZHAI, SHUAI
Format: Artikel
Sprache:eng
Schlagworte:
Alliances
Curves
Lower bounds
Market strategy
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Zusammenfassung:In this paper, we investigate the weak forms of the 2-part of the conjecture of Birch and Swinnerton-Dyer, and prove a lower bound for the 2-adic valuation of the algebraic part of the central value of the complex L -series for the family of quadratic twists of all optimal elliptic curves over ${\mathbb Q}$ .
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004118000671