Non-vanishing Theorems for Quadratic Twists of Elliptic Curves

2014/08/31 by Shuai Zhai, Zhai, Shuai
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1409.0231

Published version

openalex publication_date 2014/08/31 · arxiv created 2017/12/03 · arxiv updated 2017/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that, by applying some results on modular symbols, for a family of certain elliptic curves defined over \mathbb Q, there is a large class of explicit quadratic twists whose complex L-series does not vanish at s=1, and for which the 2-part of Birch-Swinnerton-Dyer conjecture holds.

Citations

• Modular Elliptic Curves and Fermat's Last Theorem

Related

• On the 2-part of the Birch and Swinnerton-Dyer conjecture for quadratic twists of elliptic curves
• Non-vanishing of central L-values of the Gross family of elliptic curve
• Generalized Birch lemma and the 2-part of the Birch and Swinnerton-Dyer conjecture for certain elliptic curves
• Quadratic Twists of Elliptic Curves
• Non-vanishing theorems for central L-values of some elliptic curves with complex multiplication II