Geodesic
The second moment of $\mathrm {GL}(n)\times \mathrm {GL}(n)$ Rankin–Selberg L-functions
Forum of Mathematics, Sigma, Tome 10 (2022)

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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 that is tending to infinity. Our proof uses the integral representations of the L-functions, period with regularised Eisenstein series and the invariance properties of the analytic newvectors. 
@article{10_1017_fms_2022_39,
     author = {Subhajit Jana},
     title = {The second moment of $\mathrm {GL}(n)\times \mathrm {GL}(n)$ {Rankin{\textendash}Selberg} {L-functions}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {10},
     year = {2022},
     doi = {10.1017/fms.2022.39},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.39/}
}
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Subhajit Jana. The second moment of $\mathrm {GL}(n)\times \mathrm {GL}(n)$ Rankin–Selberg L-functions. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.39

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