Chen, Shih-Yu; Cheng, Yao

On Deligne's Conjecture for Certain Automorphic \(L\)-Functions for \(\mathrm{GL}(3)\times\mathrm{GL}(2)\) and \(\mathrm{GL}(4)\)

Doc. Math. 24, 2241-2297 (2019)
DOI: 10.25537/dm.2019v24.2241-2297
Communicated by Don Blasius

Summary

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 \(\mathbb{Q}\).

Mathematics Subject Classification

11F41, 11F67

Keywords/Phrases

Deligne's conjecture, automorphic \(L\)-function, Ichino's formula

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Affiliation

Chen, Shih-Yu
Institute of Mathematics, Academia Sinica, No. 1, Sec. 4, Roosevelt R., Taipei 10617, Taiwan, ROC
Cheng, Yao
Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge R., Singapore 119076

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