$p$-adic quotient sets II: quadratic forms

Christopher Donnay, Stephan Ramon Garcia, Jeremy Rouse

For $A\subseteq \{1,2,\dots \}$, we consider $R(A)=\{a/a^{\prime }:a,a^{\prime }\in A\}$. If $A$ is the set of nonzero values assumed by a quadratic form, when is $R(A)$ dense in the $p$-adic…