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

  • Shih-Yu Chen

    Institute of Mathematics, Academia Sinica, No. 1, Sec. 4, Roosevelt R., Taipei 10617, Taiwan, ROC
  • Yao Cheng

    Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge R., Singapore 119076
On Deligne's Conjecture for Certain Automorphic $L$-Functions for $\mathrm{GL}(3)\times\mathrm{GL}(2)$ and $\mathrm{GL}(4)$ cover
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Abstract

We prove Deligne's conjecture for certain automorphic LL-functions for GL(3)×GL(2)\mathrm{GL}(3)\times\mathrm{GL}(2) and GL(4)\mathrm{GL}(4). The proof is based on rationality results for central critical values of triple product LL-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\mathbb{Q}.

Cite this article

Shih-Yu Chen, Yao Cheng, On Deligne's Conjecture for Certain Automorphic LL-Functions for GL(3)×GL(2)\mathrm{GL}(3)\times\mathrm{GL}(2) and GL(4)\mathrm{GL}(4). Doc. Math. 24 (2019), pp. 2241–2297

DOI 10.4171/DM/725