Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Average rank of elliptic curves   Bhargava and Shankar prove that as E varies over all elliptic curves over Q,
the average rank of the finitely generated abelian group E(Q) is bounded. This
result follows from an exact formula for the average size of the 2-Selmer
group, which in turn follows from an asymptotic formula for the number of
binary quartic forms over Z with bounded invariants. We explain their proof, as
well as other arithmetic applications.

15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an