On Deligne's Conjecture for Certain Automorphic -Functions for and
Shih-Yu ChenInstitute of Mathematics, Academia Sinica, No. 1, Sec. 4, Roosevelt R., Taipei 10617, Taiwan, ROC
Yao ChengDepartment of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge R., Singapore 119076
We prove Deligne's conjecture for certain automorphic -functions for and . The proof is based on rationality results for central critical values of triple product -functions, which follow from establishing explicit Ichino's formulae for trilinear period integrals for Hilbert cusp forms on totally real étale cubic algebras over .
Cite this article
Shih-Yu Chen, Yao Cheng, On Deligne's Conjecture for Certain Automorphic -Functions for and . Doc. Math. 24 (2019), pp. 2241–2297DOI 10.4171/DM/725