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

Shih-Yu Chen; Yao Cheng

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

Number Theory 2018-06-28 v2

Authors: Shih-Yu Chen , Yao Cheng

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 $\mathbb{Q}$ .

Keywords

Deligne's conjecture automorphic L-functions GL(3)xGL(2) central critical values triple product L-functions Ichino's formula Hilbert cusp forms

Cite

@article{arxiv.1806.09767,
  title  = {On Deligne's conjecture for certain automorphic $L$-functions for ${\rm GL}(3)\times {\rm GL}(2)$},
  author = {Shih-Yu Chen and Yao Cheng},
  journal= {arXiv preprint arXiv:1806.09767},
  year   = {2018}
}

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