Spectral reciprocity for $\mathrm{GL}(n)$ and simultaneous non-vanishing of central $L$-values

Subhajit Jana, Ramon Nunes

Let $F$ be a totally real number field and $n\ge 3$. Let $\Pi$ and $\pi$ be cuspidal automorphic representations for ${\mathrm{PGL}}_{n+1}(F)$ and ${\mathrm{PGL}}_{n-1}(F)$, respectively,…