Geodesic
On Deligne's Conjecture for Certain Automorphic $L$-Functions for $\mathrm{GL}(3)\times\mathrm{GL}(2)$ and $\mathrm{GL}(4)$
Documenta mathematica, Tome 24 (2019), pp. 2241-2297.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We prove Deligne's conjecture for certain automorphic $L$-functions for $\mathrm{GL}(3)\times\mathrm{GL}(2)$ and $\mathrm{GL}(4)$. The proof is based on rationality results for central critical values of triple product $L$-functions, which follow from establishing explicit Ichino's formulae for trilinear period integrals for Hilbert cusp forms on totally real étale cubic algebras over $\mathbb{Q}$.
Classification : 11F41, 11F67
Keywords: Deligne's conjecture, automorphic \(L\)-function, Ichino's formula 
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     author = {Chen, Shih-Yu and Cheng, Yao},
     title = {On {Deligne's} {Conjecture} for {Certain} {Automorphic} {\(L\)-Functions} for {\(\mathrm{GL}(3)\times\mathrm{GL}(2)\)} and {\(\mathrm{GL}(4)\)}},
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Chen, Shih-Yu; Cheng, Yao. On Deligne's Conjecture for Certain Automorphic \(L\)-Functions for \(\mathrm{GL}(3)\times\mathrm{GL}(2)\) and \(\mathrm{GL}(4)\). Documenta mathematica, Tome 24 (2019), pp. 2241-2297. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a10/