Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The irrationality measure of $\pi$ as seen through the eyes of $\cos(n)$   For different values of $\gamma \geq 0$, analysis of the end behavior of the
sequence $a_n = \cos (n)^{n^\gamma}$ yields a strong connection to the
irrationality measure of $\pi$. We show that if $\limsup |\cos n|^{n^2} \neq
1$, then the irrationality measure of $\pi$ is exactly 2. We also give some
numerical evidence to support the conjecture that $\mu(\pi)=2$, based on the
appearance of some startling subsequences of $\cos(n)^n$.

26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
18
The categories of this paper are: econ