论文标题
$ \ mathrm {gl}（n）\ Times \ Mathrm {gl}（n）$ rankin-selberg $ l $ functions的第二瞬间
The second moment of $\mathrm{GL}(n)\times\mathrm{GL}(n)$ Rankin--Selberg $L$-functions
论文作者
论文摘要
我们证明了$ \ mathrm {gl}（n）\ times \ times \ mathrm {gl}（n）$ rankin-selberg $ l $ l $ l $ l（1/2，π\otimesπ_0）$ $ wistery $ withy $ wishertion $ wishtion $ withy $ wishtion $ withytime $ wishtion $ wishtiony $ wishtiony $ withtimity $ phiptimity，导体以趋向于无穷大的数量界定。我们的证明使用了$ L $ functions的整体表示，带有正规的Eisenstein系列的时期以及分析新向量的不变性属性。
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 $L(1/2,π\otimesπ_0)$, for a fixed cuspidal automorphic representation $π_0$, over the family of $π$ 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.
