Non-vanishing Theorems for Quadratic Twists of Elliptic Curves

Shuai Zhai

Non-vanishing Theorems for Quadratic Twists of Elliptic Curves

Number Theory 2017-12-05 v2

Authors: Shuai Zhai

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.

Keywords

elliptic curves quadratic twists non-vanishing theorems modular symbols L-series Birch-Swinnerton-Dyer conjecture

Cite

@article{arxiv.1409.0231,
  title  = {Non-vanishing Theorems for Quadratic Twists of Elliptic Curves},
  author = {Shuai Zhai},
  journal= {arXiv preprint arXiv:1409.0231},
  year   = {2017}
}

Comments

Published version

Related papers

View all related →