This paper is an extension of Kim et al. (2020a), and we prove equidistribution theorems for families of holomorphic Siegel cusp forms of general degree in the level aspect. Our main contribution is to estimate unipotent contributions for general degree in the geometric side of Arthur’s invariant trace formula in terms of Shintani zeta functions in a uniform way. Several applications, including the vertical Sato–Tate theorem and low-lying zeros for standard $L$-functions of holomorphic Siegel cusp forms, are discussed. We also show that the “nongenuine forms”, which come from nontrivial endoscopic contributions by Langlands functoriality classified by Arthur, are negligible.

本文是 Kim 等人的延伸。 (2020a)，我们在水平方面证明了一般度的全纯 Siegel 尖点形式族的等分布定理。我们的主要贡献是以统一的方式根据 Shintani zeta 函数估计 Arthur 不变迹公式的几何方面的一般程度的单能贡献。多种应用，包括垂直佐藤-泰特定理和标准的低洼零点$L$-讨论了全纯西格尔尖点形式的功能。我们还表明，来自亚瑟分类的朗兰兹函子性的重要内窥镜贡献的“非真实形式”可以忽略不计。