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Relative Trace Formula, Subconvexity and Quantitative Nonvanishing of Rankin-Selberg $L$-functions for $\mathrm{GL}(n+1)\times\mathrm{GL}(n)$
We establish hybrid subconvexity bounds and quantitative simultaneous nonvanishing for Rankin--Selberg $L$-functions on $\mathrm{GL}(n+1)\times\mathrm{GL}(n)$ over $\mathbb Q$. For a fixed unitary cuspidal representation $π'$ of $\mathrm{GL}(n)$ and any unitary pure isobaric representation $π$ of $\
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