Abstract
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 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.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
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