Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of representations of squares by integral ternary quadratic
  forms   Let $f$ be a positive definite integral ternary quadratic form and let
$r(k,f)$ be the number of representations of an integer $k$ by $f$. In this
article we study the number of representations of squares by $f$. We say the
genus of $f$, denoted by $\text{gen}(f)$, is indistinguishable by squares if
for any integer $n$, $r(n^2,f)=r(n^2,f')$ for any quadratic form $f' \in
\text{gen}(f)$. We find some non trivial genera of ternary quadratic forms
which are indistinguishable by squares. We also give some relation between
indistinguishable genera by squares and the conjecture given by Cooper and Lam,
and we resolve their conjecture completely.

23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex