Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds of the Mertens Function   In this paper, we derive new properties of the Mertens function and discuss a
likely upper bound of the absolute value of the Mertens function
$\sqrt{\log{x!}}>|M(x)|$ when $x>1$. Using this likely bound we show that we
have a sufficient condition to prove the Riemann Hypothesis.

34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th