Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-vanishing Theorems for Quadratic Twists of Elliptic Curves   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.

8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys