The second moment GL(n) × GL(n) Rankin-Selberg L-functions

Jana, Subhajit

doi:10.1017/fms.2022.39

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

The second moment GL(n) × GL(n) Rankin-Selberg L-functions

MPS-Authors

/persons/resource/persons262752

Jana, Subhajit
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1017/fms.2022.39
(Publisher version)

https://doi.org/10.48550/arXiv.2012.07817
(Preprint)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

Jana_The second moment GL(n)×GL(n) Rankin-Selberg L-functions_2022.pdf
(Publisher version), 555KB

Supplementary Material (public)

There is no public supplementary material available

Citation

Jana, S. (2022). The second moment GL(n) × GL(n) Rankin-Selberg L-functions. Forum of Mathematics, Sigma, 10: e47. doi:10.1017/fms.2022.39.

Cite as: https://hdl.handle.net/21.11116/0000-000A-B040-6

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.