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Spectral Moment Formulae for hbox{GL}(3)times hbox{GL}(2) hbox{L}-functions II: The Eisenstein Case
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Spectral Moment Formulae for hbox{GL}(3)times hbox{GL}(2) hbox{L}-functions II: The Eisenstein Case
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This work is the second in a series, following Part I (Algebra Number Theory 18.10 (2024)) and preceding Part III (Math. Ann. 391.1 (2025)). We continue our investigation of spectral moments of $\hbox{GL}(3)\times \hbox{GL}(2)$ $\hbox{L}$-functions from the perspective of period integrals. Using an identity between two distinct periods for the $\hbox{GL}(3)$ Eisenstein series, we establish an exact Motohashi-type identity linking the shifted cubic moment of $\hbox{GL}(2)$ $\hbox{L}$-functions to the shifted fourth moment of $\hbox{GL}(1)$ $\hbox{L}$-functions. In addition, we offer a novel, intrinsic and automorphic account for the sources and symmetries of the full set of main terms for both moments, in agreement with the CFKRS Moment Conjectures (Proc. Lond. Math. Soc.(3) 91 (2005)).
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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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