Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An elementary proof of a power series identity for the weighted sum of
  all finite abelian p-groups   Using combinatorial techniques, we prove that the weighted sum of the inverse
number of automorphisms of all finite abelian $p$-groups $\sum_G |G|^{-u}
|\text{Aut}(G)|^{-1}$ is equal to
$\prod_{j=u+1}^\infty\left(1-1/p^j\right)^{-1}$, where $u$ is a non-negative
integer. This result was originally obtained by H. Cohen and H. W. Lenstra, Jr.
In this paper we give a new elementary proof of their result.

14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin