  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) 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.
