论文标题
确定的正交模块化形式：计算，偏移和发现
Definite orthogonal modular forms: Computations, Excursions and Discoveries
论文作者
论文摘要
我们考虑了连接到较低级别和非平凡水平的确定正交组的模块化形式的空间，该群体配备了由Kneser Neighbors定义的Hecke操作员。在回顾了使用这些空间计算算法以计算这些空间之后，我们使用theta系列和Rallis定理研究了内窥镜检查。一路上，我们展示了许多例子并提出了几个猜想。作为第一个应用，我们就经典或西格尔模块化形式的系数表达了对邻居的计数，并补充了Chenevier-Lannes的工作。作为第二个应用程序，我们证明了Ramanujan和Kurokawa-Mizumoto类型的Eisenstein一致性的新实例。
We consider spaces of modular forms attached to definite orthogonal groups of low even rank and nontrivial level, equipped with Hecke operators defined by Kneser neighbours. After reviewing algorithms to compute with these spaces, we investigate endoscopy using theta series and a theorem of Rallis. Along the way, we exhibit many examples and pose several conjectures. As a first application, we express counts of Kneser neighbours in terms of coefficients of classical or Siegel modular forms, complementing work of Chenevier-Lannes. As a second application, we prove new instances of Eisenstein congruences of Ramanujan and Kurokawa-Mizumoto type.
