Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions I: The Cuspidal Case

Abstract

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.

arXiv commentAccepted Version; 2nd half of v3 will appear as separate papers

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Cited by in corpus (3)

• $L^p$-Norm Bounds for Automorphic Forms via Spectral Reciprocity
• Strong Hybrid Subconvexity for Twisted Selfdual ${\mathrm{GL}}_3$ $L$-Functions
• Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions II: The Eisenstein Case