Generating sets for maximal orders in rational quaternion algebras

Given a maximal order $\mathfrak{O}$ in a rational definite quaternion algebra, and a prime $\ell$ coprime to the discriminant of $\mathfrak{O}$, this paper considers subsets of $\mathfrak{O}$ consisting of elements with $\ell$-power norms that together generate $\mathfrak{O}$ as a $\mathbb{Z}$-alge