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 ${\Lambda }^{\times }$.

13 pages