  We show that the absolute value $|f|$ of an invertible holomorphic function
$f$ on the Drinfeld symmetric space $\OM^r$ $(r \geq 2)$ is constant on fibers
of the building map to the Bruhat-Tits building $\MB\MT$. Its logarithm
$\log|f|$ is an affine map on the realization of $\MB\MT$. These results are
used to study the vanishing loci of modular forms (coefficient forms,
Eisenstein series, para-Eisenstein series) and to determine their images in
$\MB\MT$.
