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Spectral Moment Formulae for GL(3)times GL(2) L-functions I: The Cuspidal Case
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Spectral Moment Formulae for GL(3)times GL(2) L-functions I: The Cuspidal Case
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Spectral moment formulae of various shapes have proven to be very successful in studying the statistics of central $L$-values. In this article, we establish, in a completely explicit fashion, such formulae for the family of $GL(3)\times GL(2)$ Rankin-Selberg $L$-functions using the period integral method. The Kuznetsov and the Voronoi formulae are not needed in our argument. We also prove the essential analytic properties and explicit formulae for the integral transform of our moment formulae. It is hoped that our method will provide insights into moments of $L$-functions for higher-rank groups.
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Cited by 1 Pith paper
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Strong Hybrid Subconvexity for Twisted Selfdual $\mathrm{GL}_3$ $L$-Functions
Establishes strong hybrid subconvexity bounds for twisted selfdual GL3 L-functions via a new GL3 x GL2 to GL4 x GL1 spectral reciprocity formula together with an averaged Lindelof bound on Dirichlet L-functions.
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