  Let $u$ be a nowhere vanishing holomorphic function on the Drinfeld space
$\Omega^{r}$ of dimension $r-1$, where $r \geq 2$. The logarithm
$\log_{q}\lvert u \rvert$ of its absolute value may be regarded as an affine
function on the attached Bruhat-Tits building $\mathcal{BT}^{r}$. Generalizing
a construction of van der Put in case $r=2$, we relate the group
$\mathcal{O}(\Omega^{r})^{*}$ of such $u$ with the group
$\mathbf{H}(\mathcal{BT}^{r}, \mathbb{Z})$ of integer-valued harmonic
1-cochains on $\mathcal{BT}^{r}$. This also gives rise to a natural
$\mathbb{Z}$-structure on the first ($\ell$-adic or de Rham) cohomology of
$\Omega^{r}$.
