Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new proof for the exact values of $\zeta(2k)$ for $k \in \mathbb{N}$   We establish a connection between a function and a series representation
using a similar technique with that that Euler used to solve the Basel problem.
Our result concerns a more general series from which one can obtain $\zeta(2k)$
as a limit case. We also are able to prove the well known result expressing
$\zeta(2k)$ with Bernoulli numbers as an application.

23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph