Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growth of the analytic rank of modular elliptic curves over quintic
  extensions   Given $F$ a totally real field and $E_{/F}$ a modular elliptic curve, we
denote by $G_5(E_{/F};X)$ the number of quintic extensions $K$ of $F$ such that
the norm of the relative discriminant is at most $X$ and the analytic rank of
$E$ grows over $K$, i.e., $r_\mathrm{an}(E/K)>r_\mathrm{an}(E/F)$. We show that
$G_5(E_{/F};X)\asymp_{+\infty} X$ when the elliptic curve $E_{/F}$ has odd
conductor and at least one prime of multiplicative reduction. As Bhargava,
Shankar and Wang \cite{BSW} showed that the number of quintic extensions of $F$
with norm of the relative discriminant at most $X$ is asymptotic to $c_{5,F} X$
for some positive constant $c_{5,F}$, our result exposes the growth of the
analytic rank as a very common circumstance over quintic extensions.

27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg