Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of Goldbach representations of an integer   We prove the following result: Let $N \geq 2$ and assume the Riemann
Hypothesis (RH) holds. Then \[ \sum_{n=1}^{N} R(n) =\frac{N^{2}}{2} -2
\sum_{\rho} \frac{N^{\rho + 1}}{\rho (\rho + 1)} + O(N \log^{3}N), \] where
$\rho=1/2+i\gamma$ runs over the non-trivial zeros of the Riemann zeta function
$\zeta(s)$.

30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an