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We introduce a new trace formula of Kuznetsov type involving the centralstandard L-values and the Whittaker periods of cuspidal automorphicrepresentations of PGL_n(Q) which are spherical at the archimedean place. As anapplication, we show a simultaneous non-vanishing of standard L-values at n-1points on the critical strip for infinitely many Hecke-Maass cuspidal newforms.

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