Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An $\ell-p$ switch trick to obtain a new elementary proof of a criterion
  for arithmetic equivalence   Two number fields are called arithmetically equivalent if they have the same
Dedekind zeta function. In the 1970's Perlis showed that this is equivalent to
the condition that for almost every rational prime $\ell$ the arithmetic type
of $\ell$ is the same in each field. In the 1990's Perlis and Stuart gave an
unexpected characterization for arithmetic equivalence; they showed that to be
arithmetically equivalent it is enough for almost every prime $\ell$ to have
the same number of prime factors in each field. Here, using an $\ell-p$ switch
trick, we provide an elementary proof of that fact based on a classical result
of Smith from the 1870's.

21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas