论文标题
Weyl的任意Archimedean类型定律
Weyl's Law for Arbitrary Archimedean Type
论文作者
论文摘要
我们概括了Lindenstrauss和Venkatesh的工作，从而从球形谱系到任意的阿基米德类型建立了尖峰形式的Weyl定律。球形光谱的Weyl定律给出了一个渐近公式，用于在Laplacian的特征值T方面的双球形形式数量。我们证明了具有Archimedean typeτ的尖缘形式的类似渐近线，其中主术语乘以DIMτ。在球形案例中，使用了Satake地图的溢流性，但在不可用的情况下，我们使用了Arthur的Paley-Wiener定理和乘数。
We generalize the work of Lindenstrauss and Venkatesh establishing Weyl's Law for cusp forms from the spherical spectrum to arbitrary Archimedean type. Weyl's law for the spherical spectrum gives an asymptotic formula for the number of cusp forms that are bi-spherical in terms of eigenvalue T of the Laplacian. We prove an analogous asymptotic holds for cusp forms with Archimedean type τ, where the main term is multiplied by dim τ. While in the spherical case the surjectivity of the Satake Map was used, in the more general case that is not available and we use Arthur's Paley-Wiener theorem and multipliers.
