We show that the absolute value $|f|$ of an invertible holomor- phic function f on the Drinfeld symmetric space ${\mathrm{\Omega }}^r$ $(r\ge 2)$ is constant on fibers of the building map to the Bruhat–Tits building $\mathcal{B}\mathcal{T}$. Its logarithm $\log |f|$ is an affine map on the realization of $\mathcal{B}\mathcal{T}$. 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 $\mathcal{B}\mathcal{T}$.

中文翻译：

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关于更高阶 II 的 Drinfeld 模形式

我们证明绝对值 $|F|$Drinfeld 对称空间上的可逆全纯函数f${\mathrm{\Omega }}^r$ $(r\ge 2)$ 在建筑物映射到 Bruhat-Tits 建筑物的纤维上是恒定的 $\mathcal{乙}\mathcal{吨}$. 它的对数$\mathrm{日志}|F|$ 是实现的仿射图 $\mathcal{乙}\mathcal{吨}$. 这些结果用于研究模形式（系数形式、爱森斯坦级数、对爱森斯坦级数）的消失轨迹并确定它们在$\mathcal{乙}\mathcal{吨}$.