Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A mean value result involving the fourth moment of $|\zeta(1/2+it)|$   If $(k,\ell)$ is an exponent pair such that $k+\ell<1$, then we have $$
\int_1^T|\zeta(1/2+it)|^4|\zeta(\sigma+it)|^2dt \ll_\epsilon
T^{1+\epsilon}\quad(\sigma > \min({5\over6},\max(\ell-k, {5k+\ell\over4k+1})),
$$ while if $(k,\ell)$ is an exponent pair such that $3k+\ell<1$, then we have
$$ \int_1^T|\zeta(1/2+it)|^4|\zeta(\sigma+it)|^4dt \ll_\epsilon
T^{1+\epsilon}\quad(\sigma > {11k+\ell+1\over8k+2}). $$

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
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph