论文标题
通过内窥镜分类对统一组的共同体构造表示的统计数据
Statistics of Cohomological Automorphic Representations on Unitary Groups via the Endoscopic Classification
论文作者
论文摘要
考虑一个统一组上的自动形式代表家族，在无穷大并给定分裂水平的同源系数$π_0$上。我们计算这个家庭的统计数据，因为该水平达到了无限。对于未受到的统一组和大型$π_0$，我们使用表示表示的内窥镜分类来计算SATAKE参数的表示计数和平均值的确切指导术语。我们错误项上的界限与Shin-Templier先前的工作相似，后者研究了Infinity的离散序列案例。我们还证明了所有共同体表示的新上限。 This has many corollaries: new exact asymptotics on the growth of cohomology in certain towers of locally symmetric spaces, an averaged Sato-Tate equidistribution law for spectral families with specific non-tempered cohomological components at infinity, and the Sarnak-Xue density hypothesis for cohomological representations at infinity on all unitary groups of rank $\geq 5$.
Consider the family of automorphic representations on a unitary group with cohomological factor $π_0$ at infinity and given split level. We compute statistics of this family as the level goes to infinity. For unramified unitary groups and a large class of $π_0$, we use the endoscopic classification of representations to compute the exact leading term for counts of representations and averages of Satake parameters. The bounds on our error terms are similar to previous work by Shin-Templier who studied the case of discrete series at infinity. We also prove new upper bounds for all cohomological representations. This has many corollaries: new exact asymptotics on the growth of cohomology in certain towers of locally symmetric spaces, an averaged Sato-Tate equidistribution law for spectral families with specific non-tempered cohomological components at infinity, and the Sarnak-Xue density hypothesis for cohomological representations at infinity on all unitary groups of rank $\geq 5$.
