Hecke-Maass cusp forms on PGL_n of large levels with non-vanishing L-values

Abstract

We introduce a new trace formula of Kuznetsov type involving the central standard L-values and the Whittaker periods of cuspidal automorphic representations of PGL n (Q) (n 3) which are spherical at the archimedean place. As an application, we show a simultaneous non-vanishing of standard L-values at n − 1 points on the critical strip for infinitely many Hecke-Maass cuspidal newforms of growing prime levels.