Spectral Reciprocity for the product of Rankin-Selberg $L$-functions

Abstract

We prove a new case of spectral reciprocity formulae for the product of $GL(n+1)\times GL(n)$ and $GL(n)\times GL(n-1)$ Rankin-Selberg $L$-functions ($n\ge 3$), which are first developed by Blomer and Khan in \cite{BK17} for degree 8 $L$-functions ($n=2$ case, the product of $GL(3)\times GL(2)$ and $GL(2)\times GL(1)$ Rankin-Selberg $L$-functions). Our result can be viewed as a generalization of Blomer and Khan's work to higher rank case. We will mainly follow the method developed in \cite{Nun20}. We will use the integral representations of Rankin-Selberg $L$-functions generalized by Ichino and Yamana \cite{IY15}, spectral theory of $L^2$ space and the language of automorphic representations.

31 pages. This is a preliminary draft. All comments are welcome!

References in corpus (3)

• Eisenstein series and the cubic moment for PGL(2)
• Periods and Reciprocity II
• Subconvexity bounds for twisted L-functions, II