Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $p$-adic quotient sets II: quadratic forms   For $A \subseteq \{1,2,\ldots\}$, we consider $R(A) = \{a/a' : a,a' \in A\}$.
If $A$ is the set of nonzero values assumed by a quadratic form, when is $R(A)$
dense in the $p$-adic numbers? We show that for a binary quadratic form $Q$,
$R(A)$ is dense in $\mathbb{Q}_{p}$ if and only if the discriminant of $Q$ is a
nonzero square in $\mathbb{Q}_{p}$, and for a quadratic form in at least three
variables, $R(A)$ is always dense in $\mathbb{Q}_{p}$. This answers a question
posed by several authors in 2017.

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The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex