标题： 关于高秩德林函数模形式第七部分：边界处的展开 显示英文标题

标题： On Drinfeld modular forms of higher rank VII: Expansions at the boundary

摘要： 我们研究了在模空间边界上Drinfeld模形式的展开，其秩为\(r \geq 2\)。 判别式形式\(\Delta_{\mathfrak{n}}\)的乘积公式被建立，这与Jacobi的经典椭圆判别式的公式类似。 通过底层Drinfeld系数环\(A\)在\(s=1-r\)处的部分zeta函数的值来描述消去阶。 我们证明了Eisenstein级数的线性无关性，这使得可以将模形式的空间分解为尖点形式子空间和Eisenstein级数子空间，并给出了模形式边界条件的各种特征。 显示英文摘要

摘要： We study expansions of Drinfeld modular forms of rank \(r \geq 2\) along the boundary of moduli varieties. Product formulas for the discriminant forms \(\Delta_{\mathfrak{n}}\) are developed, which are analogous with Jacobi's formula for the classical elliptic discriminant. The vanishing orders are described through values at \(s=1-r\) of partial zeta functions of the underlying Drinfeld coefficient ring \(A\). We show linear independence properties for Eisenstein series, which allow to split spaces of modular forms into the subspaces of cusp forms and of Eisenstein series, and give various characterizations of the boundary condition for modular forms.