Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Noether's rationality problem for cyclic groups over $\mathbb{Q}$   Let $p$ be a prime number. Let $C_p$, the cyclic group of order $p$, permute
transitively a set of indeterminates $\{ x_1,\ldots ,x_p \}$. We prove that the
invariant field $\mathbb{Q}(x_1,\ldots ,x_p)^{C_p}$ is rational over
$\mathbb{Q}$ if and only if the $(p-1)$-th cyclotomic field
$\mathbb{Q}(\zeta_{p-1})$ has class number one.

21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat