The second moment of $\mathrm{GL}(n)\times \mathrm{GL}(n)$ Rankin--Selberg $L$-functions

Abstract

We prove an asymptotic expansion of the second moment of the central values of the $\mathrm{GL}(n)\times \mathrm{GL}(n)$ Rankin--Selberg $L$-functions $L(1/2,\pi \otimes {\pi }_0)$, for a fixed cuspidal automorphic representation ${\pi }_0$, over the family of $\pi$ with analytic conductors bounded by a quantity which is tending off to infinity. Our proof uses the integral representations of the $L$-functions, period with regularized Eisenstein series, and the invariance properties of the analytic newvectors.

44 pages, to appear in Forum math, Sigma

References in corpus (2)

• Upper bounds on L-functions at the edge of the critical strip
• The sixth moment of automorphic $L$-functions

Cited by in corpus (1)

• Zeros of Rankin-Selberg $L$-functions in families