Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On some $q$-series identities related to a generalized divisor function
  and their implications   In this article, a $q$-series examined by Kluyver and Uchimura is
generalized. This allows us to find generalization of the identities in the
random acyclic digraph studied by Simon, Crippa, and Collenberg in 1993. As one
of the corollaries of our main theorem, we get results of Dilcher and Andrews,
Crippa, and Simon. This main theorem involves a surprising new generalization
of the divisor function $\sigma_s(n)$, which we denote by $\sigma_{s,z}(n)$.
Analytic properties of $\sigma_{s,z}(n)$ are also studied. As a special case of
one of our theorem we obtain result from a recent paper of Bringmann and
Jennings-Shaffer.

20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
19
The categories of this paper are: eess
9
The categories of this paper are: nlin