On generators of arithmetic groups over function fields

Abstract

Let $F=\mathbb{F}_q(T)$ be the field of rational functions with $\mathbb{F}_q$-coefficients, and $A=\mathbb{F}_q[T]$ be the subring of polynomials. Let $D$ be a division quaternion algebra over $F$ which is split at $1/T$. Given an $A$-order $\Lambda$ in $D$, we find an explicit finite set generating $\Lambda^\times$.