  In this article, we give an explicit description of the invertible functions
on the Drinfeld symmetric space over $K$ a finite extension of $\mathbb{Q}_p$.
We identify them with some distribution spaces over the profinite set of
$K$-rationnal points of the projective space. The strategy consists of
constructing a map from these distributions to the invertible functions
following the methods of Schneider-Stuhler, Iovita-Spiess, de Shalit. We show
that it is compatible with the isomorphisms they constructed to compute \'etale
and de Rham cohomology in degree $1$ and that this property forces our desired
map to be an isomorphism. In particular, we get a $\mathbb{Z}$-structure on
these cohomology groups.
