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
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We prove Deligne's conjecture for certain automorphic L-functions for GL(3)×GL(2) and 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 Q.
DOI : 10.4171/dm/725
Classification : 11F41, 11F67
Mots-clés : Deligne's conjecture, automorphic L-function, Ichino's formula 
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     author = {Shih-Yu Chen and Yao Cheng},
     title = {On {Deligne's} {Conjecture} for {Certain} {Automorphic} $L${-Functions} for $\mathrm{GL}(3)\times\mathrm{GL}(2)$ and $\mathrm{GL}(4)$},
     journal = {Documenta mathematica},
     pages = {2241--2297},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/725},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/725/}
}
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Shih-Yu Chen; Yao Cheng. 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. doi: 10.4171/dm/725

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