Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ramanujan-type Congruences for Overpartitions Modulo 16   Let $\overline{p}(n)$ denote the number of overpartitions of $n$. Recently,
Fortin-Jacob-Mathieu and Hirschhorn-Sellers independently obtained 2-, 3- and
4-dissections of the generating function for $\overline{p}(n)$ and derived a
number of congruences for $\overline{p}(n)$ modulo $4$, $8$ and $64$ including
$\overline{p}(5n+2)\equiv 0 \pmod{4}$, $\overline{p}(4n+3)\equiv 0 \pmod{8}$
and $\overline{p}(8n+7)\equiv 0 \pmod{64}$. By employing dissection techniques,
Yao and Xia obtained congruences for $\overline{p}(n)$ modulo $8, 16$ and $32$,
such as $\overline{p}(48n+26) \equiv 0 \pmod{8}$, $\overline{p}(24n+17)\equiv 0
\pmod{16}$ and $\overline{p}(72n+69)\equiv 0 \pmod{32}$. In this paper, we give
a 16-dissection of the generating function for $\overline{p}(n)$ modulo 16 and
we show that $\overline{p}(16n+14)\equiv0\pmod{16}$ for $n\ge 0$. Moreover, by
using the $2$-adic expansion of the generating function of $\overline{p}(n)$
due to Mahlburg, we obtain that $\overline{p}(\ell^2n+r\ell)\equiv0\pmod{16}$,
where $n\ge 0$, $\ell \equiv -1\pmod{8}$ is an odd prime and $r$ is a positive
integer with $\ell \nmid r$. In particular, for $\ell=7$, we get
$\overline{p}(49n+7)\equiv0\pmod{16}$ and
$\overline{p}(49n+14)\equiv0\pmod{16}$ for $n\geq 0$. We also find four
congruence relations: $\overline{p}(4n)\equiv(-1)^n\overline{p}(n) \pmod{16}$
for $n\ge 0$, $\overline{p}(4n)\equiv(-1)^n\overline{p}(n)\pmod{32}$ for $n$
being not a square of an odd positive integer,
$\overline{p}(4n)\equiv(-1)^n\overline{p}(n)\pmod{64}$ for $n\not\equiv
1,2,5\pmod{8}$ and $\overline{p}(4n)\equiv(-1)^n\overline{p}(n)\pmod{128}$ for
$n\equiv 0\pmod{4}$.

20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin