Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic harmonic behavior in the prime number distribution   We consider $\Phi(x)=x^{-\frac{1}{4}}\left[1-2\sqrt{x}\Sigma e^{-p^2\pi x}\ln
p\right]$ on $x>0$, where the sum is over all primes $p$. If $\Phi$ is bounded
on $x>0$, then the Riemann hypothesis is true or there are infinitely many
zeros Re~$z_k>\frac{1}{2}$. The first 21 zeros give rise to asymptotic harmonic
behavior in $\Phi(x)$ defined by the prime numbers up to one trillion.

9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th