Moments of $L$-functions via a relative trace formula

Subhajit Jana, Ramon Nunes

We prove an asymptotic formula for the second moment of the $\mathrm{GL}(n)\times \mathrm{GL}(n+1)$ Rankin--Selberg central $L$-values $L(1/2,\Pi \otimes \pi )$, where $\pi$ is a fixed cuspi…