Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moments of the critical values of families of elliptic curves, with
  applications   We make conjectures on the moments of the central values of the family of all
elliptic curves and on the moments of the first derivative of the central
values of a large family of positive rank curves. In both cases the order of
magnitude is the same as that of the moments of the central values of an
orthogonal family of L-functions. Notably, we predict that the critical values
of all rank 1 elliptic curves is logarithmically larger than the rank 1 curves
in the positive rank family.
  Furthermore, as arithmetical applications we make a conjecture on the
distribution of a_p's amongst all rank 2 elliptic curves, and also show how the
Riemann hypothesis can be deduced from sufficient knowledge of the first moment
of the positive rank family (based on an idea of Iwaniec).

24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th