Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cubic twin prime polynomials are counted by a modular form   We present the geometry lying behind counting twin prime polynomials in
$\mathbb{F}_q[T]$ in general. We compute cohomology and explicitly count points
by means of a twisted Lefschetz trace formula applied to these parametrizing
varieties for cubic twin prime polynomials. The elliptic curve $X^3 = Y(Y-1)$
occurs in the geometry, and thus counting cubic twin prime polynomials involves
the associated modular form. In theory, this approach can be extended to higher
degree twin primes, but the computations become harder.
  The formula we get in degree $3$ is compatible with the Hardy-Littlewood
heuristic on average, agrees with the prediction for $q \equiv 2 \pmod 3$ but
shows anomalies for $q \equiv 1 \pmod 3$.

15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys