We introduce a new trace formula of Kuznetsov type involving the central standard L-values and the Whittaker periods of cuspidal automorphic representations of ${\mathrm{PGL}}_n(\mathbb{Q})$ $(n⩾3)$ which are spherical at the archimedean place. As an application, we prove the existence of infinitely many Hecke-Maass cuspidal newforms of large levels whose standard L-values at $n-1$ prescribed points on the critical strip are nonvanishing.

中文翻译：

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Hecke-Maass 尖峰在具有非消失 L 值的大水平 PGLn 上形成

我们引入了一个新的 Kuznetsov 型迹公式，它涉及中心标准L 值和 Whittaker 周期的尖峰自守表示${\mathrm{PGL}}_n(\mathbb{问})$ $(n⩾3)$在阿基米德处是球形的。作为一个应用，我们证明了存在无穷多个大能级的 Hecke-Maass 尖点新形式，其标准L值为$n-1$ 临界带上的规定点不为零。