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arXiv · 1409.0231

Non-vanishing Theorems for Quadratic Twists of Elliptic Curves

Shuai Zhai
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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.

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Shuai Zhai. 2014-08-31. Non-vanishing Theorems for Quadratic Twists of Elliptic Curves. https://arxiv.org/abs/1409.0231

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