Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some explicit estimates for the error term in the prime number theorem   By combining and improving recent techniques and results, we provide explicit
estimates for the error terms $|\pi(x)-\text{li}(x)|$, $|\theta(x)-x|$ and
$|\psi(x)-x|$ appearing in the prime number theorem. For example, we show for
all $x\geq 2$ that $|\psi(x)-x|\leq 9.39x(\log x)^{1.515}\exp(-0.8274\sqrt{\log
x})$. Our estimates rely heavily on explicit zero-free regions and zero-density
estimates for the Riemann zeta-function, and improve on existing bounds for
prime-counting functions for large values of $x$.

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The categories of this paper are: chem-ph
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph