Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a question of Perlis and Stuart regarding arithmetic equivalence   Let $K$ be a number field. The $K$-arithmetic type of a rational prime $\ell$
is the tuple $A_{K}(\ell)=(f^{K}_{1},...,f^{K}_{g_{\ell}})$ of the residue
degrees of $\ell$ in $K$, written in ascending order. A well known result of
Perlis from the 70's states that two number fields have the same Dedekind zeta
function if and only if for almost all primes $\ell$ the arithmetic types of
$\ell$ in both fields coincide. By the end of the 90's Perlis and Stuart asked
if having the same zeta function implies that for ramified primes the sum of
the ramification degrees coincide. Here we study and answer their question for
septic number fields.

22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
14
The categories of this paper are: math-ph