论文标题
紧凑型算术商的自称形式的Hecke特征值的渐近学
Asymptotics for Hecke eigenvalues of automorphic forms on compact arithmetic quotients
论文作者
论文摘要
在本文中，我们描述了针对紧凑型算术商在拉普拉斯特征值方面的hecke特征值的渐近分布。我们使用傅立叶积分运算符方法，而不是依靠痕量公式（这是对该主题进行研究的主要工具）。这使我们不仅可以对待球形，而且可以处理具有相应剩余估计值的非球形Hecke-maass形式。我们的渐近公式可用于具有相同算术亚组的数字字段的任意简单和连接的代数组。
In this paper, we describe the asymptotic distribution of Hecke eigenvalues in the Laplace eigenvalue aspect for certain families of Hecke-Maass forms on compact arithmetic quotients. Instead of relying on the trace formula, which was the primary tool in preceding studies on the subject, we use Fourier integral operator methods. This allows us to treat not only spherical, but also non-spherical Hecke-Maass forms with corresponding remainder estimates. Our asymptotic formulas are available for arbitrary simple and connected algebraic groups over number fields with cocompact arithmetic subgroups.
