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.
A zero-density estimate for $L$-functions associated with $\rm GL(3)$ Hecke--Maass cusp forms
Joint cubic moment of Eisenstein series and Hecke-Maass cusp forms
On Signs of Fourier Coefficients of Hecke-Maass Cusp Forms on $\mathrm{GL}_3$
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