Let $D=\left(\frac{a,b}{\mathbb{Q}}\right)$ be a quaternion algebra over $\mathbb{Q}$. Suppose $D$ is ramified at a finite set $S$ of places and $\infty\in S$. It is known that the $S$-units (the unit group $R_S^1$ of a maximal $\mathcal{O}_S$-order $R_S$) is finite (see Voight's Quaterinon Algebras Proposition 32.3.7 on page 595).
Is there any formula for the cardinality of $R_S^1$? Or any covolume formula for $R_S^1$ in $D_S^1$ where $D_S=\Pi_{p\in S}D\otimes_{\mathbb{Q}}\mathbb{Q}_p$? As an analog of Prasad, G. (1990). Semi-simple groups and arithmetic subgroups .
