Non-vanishing Theorems for Quadratic Twists of Elliptic Curves
Abstract
In this paper, we show that, by applying some results on modular symbols, for a family of certain elliptic curves defined over 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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