On Deligne's conjecture for symmetric fourth $L$-functions of Hilbert modular forms

DOI10.1016/J.AIM.2023.108860arXiv2101.07507WikidataQ123123084 ScholiaQ123123084MaRDI QIDQ6358571

Shih-Yu Chen

Publication date: 19 January 2021

Abstract: We prove an automorphic analogue of Deligne's conjecture for symmetric fourth $L$-functions of Hilbert modular forms. We extend the result of Morimoto based on generalization and refinement of the results of Grobner and Lin to cohomological irreducible essentially conjugate self-dual cuspidal automorphic representations of ${mGL}_2$ and ${mGL}_3$ over CM-fields.

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Cohomology of arithmetic groups (11F75)

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