On the 2-part of the Birch and Swinnerton-Dyer conjecture for quadratic twists of elliptic curves

Autor:	Cai, Li, Li, Chao, Zhai, Shuai
Rok vydání:	2017
Předmět:	Mathematics - Number Theory 11G05 11G40
Druh dokumentu:	Working Paper
Popis:	In the present paper, we prove, for a large class of elliptic curves defined over $\mathbb{Q}$, the existence of an explicit infinite family of quadratic twists with analytic rank $0$. In addition, we establish the $2$-part of the conjecture of Birch and Swinnerton-Dyer for many of these infinite families of quadratic twists. Recently, Xin Wan has used our results to prove for the first time the full Birch--Swinnerton-Dyer conjecture for some explicit infinite families of elliptic curves defined over $\mathbb{Q}$ without complex multiplication. Comment: 21 pages, including examples of full BSD conjecture, to appear in the Journal of the London Mathematical Society
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1712.01271 Zobrazit plný text záznamu View this record from Arxiv