论文标题
在计算$ \ mathrm {gsp}（4）$的cuspidal汽车表示
On counting cuspidal automorphic representations for $\mathrm{GSp}(4)$
论文作者
论文摘要
我们找到$ \ Mathrm {gsp}（4，\ Mathbb {a} _ {\ Mathbb {q}}）$的数字$ s_k（p，ω）$ $ \ mathrm {gsp}（gsp}（4，\ mathbb {a} _ {\ mathbb {a} _ { $ p $的组件是类型$ω$的iWahori-Spherical表示形式，否则不受影响。使用自动型Plancherel密度定理，我们展示了$ s_k（p，ω）$的公式的限制版本如何推广到矢量值情况下，以及有限数量的分支位置。
We find the number $s_k(p,Ω)$ of cuspidal automorphic representations of $\mathrm{GSp}(4,\mathbb{A}_{\mathbb{Q}})$ with trivial central character such that the archimedean component is a holomorphic discrete series representation of weight $k\ge 3$, and the non-archimedean component at $p$ is an Iwahori-spherical representation of type $Ω$ and unramified otherwise. Using the automorphic Plancherel density theorem, we show how a limit version of our formula for $s_k(p,Ω)$ generalizes to the vector-valued case and a finite number of ramified places.
