In this article, we establish an asymptotic estimate on the number of cuspidal automorphic representations of ${\mathrm{GL}}_4({\mathbb{A}}_{\mathbb{Q}})$ which contribute to the cuspidal cohomology of ${\mathrm{GL}}_4$ and are obtained from symmetric cube transfer of automorphic representations of ${\mathrm{GL}}_2({\mathbb{A}}_{\mathbb{Q}})$ of a given weight and with varying level structure. This generalises the recent work of C. Ambi about the similar problem for ${\mathrm{GL}}_3$.

中文翻译：

---

GL ₄尖瓣上同调的增长

在这篇文章中，我们建立了一个渐近估计的尖瓣自守表示的数量 ${\mathrm{GL}}_4({\mathbb{一种}}_{\mathbb{问}})$ 这有助于 ${\mathrm{GL}}_4$ 并且是从自守表示的对称立方转移获得的 ${\mathrm{GL}}_2({\mathbb{一种}}_{\mathbb{问}})$给定的重量和不同的层次结构。这概括了 C. Ambi 最近关于类似问题的工作${\mathrm{GL}}_3$.