Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a factorization of Riemann's $\zeta$ function with respect to a
  quadratic field and its computation   Let $K$ be a quadratic field, and let $\zeta_K$ its Dedekind zeta function.
In this paper we introduce a factorization of $\zeta_K$ into two functions,
$L_1$ and $L_2$, defined as partial Euler products of $\zeta_K$, which lead to
a factorization of Riemann's $\zeta$ function into two functions, $p_1$ and
$p_2$. We prove that these functions satisfy a functional equation which has a
unique solution, and we give series of very fast convergence to them. Moreover,
when $\Delta_K>0$ the general term of these series at even positive integers is
calculated explicitly in terms of generalized Bernoulli numbers.

5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ