Algebraicity of the near central non-critical values of symmetric fourth L-functions for Hilbert modular forms

Let Π be a cohomological irreducible cuspidal automorphic representation of GL2(AF) with central character ωΠ over a totally real number field F. In this paper, we prove the algebraicity of the near central non-critical value of the symmetric fourth L-function of Π twisted by ωΠ−2. The algebraicity...

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Bibliographic Details
Published in:Journal of number theory 2022-02, Vol.231, p.269-315
Main Author: Chen, Shih-Yu
Format: Article
Language:English
Subjects:
Special values of L-functions
Whittaker periods for [formula omitted]
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Summary:Let Π be a cohomological irreducible cuspidal automorphic representation of GL2(AF) with central character ωΠ over a totally real number field F. In this paper, we prove the algebraicity of the near central non-critical value of the symmetric fourth L-function of Π twisted by ωΠ−2. The algebraicity is expressed in terms of the Petersson norm of the normalized newform of Π and the top degree Whittaker period of the Gelbart–Jacquet lift Sym2Π of Π.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2021.05.002