Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A disproof of the Riemann Hypothesis via the Nicolas Criterion   The achievement of this paper is a confutation of the inequality addressed by
the Nicolas criterion for the Riemann Hypothesis, carried out after
establishing properties of two related sequences. One of them is the product
$\prod_{k=1}^n(1-1/p_k)$, rewritten as an alternating sum. The disproof is by
contradiction: assuming the Nicolas inequality is always true, we reach an
absurdity exploiting the aforementioned properties and a general lemma.

20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat