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arXiv · 1806.09767

On Deligne's conjecture for certain automorphic $L$-functions for ${\rm GL}(3)\times {\rm GL}(2)$

Shih-Yu Chen·Yao Cheng
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Abstract

We prove Deligne's conjecture for central critical values of certain automorphic $L$-functions for ${\rm GL}(3)\times {\rm GL}(2)$. The proof is base 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 etale cubic algebras over $\mathbb{Q}$.

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Shih-Yu Chen, Yao Cheng. 2018-06-26. On Deligne's conjecture for certain automorphic $L$-functions for ${\rm GL}(3)\times {\rm GL}(2)$. https://arxiv.org/abs/1806.09767

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