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arXiv · 2110.11529

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

Xinchen Miao
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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 ($n \geq 3$), 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.

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Xinchen Miao. 2021-10-22. Spectral Reciprocity for the product of Rankin-Selberg $L$-functions. https://arxiv.org/abs/2110.11529

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