Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Fiber Characters of $\mathbb F^*_{p^m}$ and related Polynomial
  Algebras   Let $p$ be a prime, $m$ be a positive integer ( $m \geq 1$, and $m \geq 2$ if
$p=2$), and $\chi_n$ be a multiplicative complex character on $\mathbb
F^*_{p^m}$ with order $n| (p^m-1)$. We show that a partition $\mathcal A_1 \cup
\mathcal A_2 \cup \cdots \cup \mathcal A_n$ of $\mathbb F^{*}_{p^m}$ is the
partition by fibers of $\chi_n$ if and only if these fibers %$\mathcal A_i$
satisfy certain additive properties. This is equivalent to show that the set of
multivariate characteristic polynomials of these fibers, completed with the
constant polynomial $1$, is the basis of a $(n+1)$-dimensional commutative
algebra with identity in the ring $\mathbb Q[x_1,\ldots,x_n]/\langle x_1^p-1,
\ldots, x_n^p-1 \rangle$.

35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs