论文标题
关于一般矢量值模块形式的计算
On the Computation of General Vector-valued Modular Forms
论文作者
论文摘要
我们介绍并讨论一种算法及其实现，该算法能够直接确定任何矢量值模块化的权重形式的傅立叶扩展，至少与核心是一致性亚组的表示相关的$ 2 $。它补充了两种可用的算法，这些算法仅限于归纳的dirichlet字符和Weil表示形式，从而涵盖了Moonshine或Jacobi表单等进一步的应用程序，以获取一致性子组。我们通过排列组的技术检查了特定表示中不变的计算，这极大地有助于运行时性能。我们解释了经典模块化形式的尖峰扩展的概括如何进入我们的实施。在考虑了时间复杂性之后，我们将我们的算法的表述与两个可用的算法联系起来，以突出显示每个算法的一般性和每个它们所产生的概念之间的妥协。
We present and discuss an algorithm and its implementation that is capable of directly determining Fourier expansions of any vector-valued modular form of weight at least $2$ associated with representations whose kernel is a congruence subgroup. It complements two available algorithms that are limited to inductions of Dirichlet characters and to Weil representations, thus covering further applications like Moonshine or Jacobi forms for congruence subgroups. We examine the calculation of invariants in specific representations via techniques from permutation groups, which greatly aids runtime performance. We explain how a generalization of cusp expansions of classical modular forms enters our implementation. After a heuristic consideration of time complexity, we relate the formulation of our algorithm to the two available ones, to highlight the compromises between level of generality and performance that each them makes.
