Journal of Number Theory ( IF 0.6 ) Pub Date : 2019-05-20 , DOI: 10.1016/j.jnt.2019.04.019 Ernst-Ulrich Gekeler
We construct and study a natural compactification of the moduli scheme for rank-r Drinfeld -modules with a structure of level . Namely, , the projective variety associated with the graded ring generated by the Eisenstein series of rank r and level N. We use this to define the ring of all modular forms of rank r and level N. It equals the integral closure of in their common quotient field . Modular forms are characterized as those holomorphic functions on the Drinfeld space with the right transformation behavior under the congruence subgroup of (“weak modular forms”) which, along with all their conjugates under , are bounded on the natural fundamental domain F for Γ on .
中文翻译:
关于更高阶 IV 的 Drinfeld 模形式:具有水平的模形式
我们构建并研究自然压实 模数方案的 对于 rank- r Drinfeld-具有层次结构的模块 . 即,, 与分级环相关的射影变异 由秩为r和水平为N的爱森斯坦级数生成。我们用它来定义环等级r和等级N的所有模形式。它等于的积分闭包 在它们的公商域中 . 模形式被表征为 Drinfeld 空间上的那些全纯函数 在同余子群下具有正确的变换行为 的 (“弱模形式”),连同它们在 , 有界于Γ on的自然基域F.