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

Shih-Yu Chen

doi:10.1016/j.jnt.2021.05.002

期刊文章

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

Shih-Yu Chen

Journal of Number Theory, 卷.231, 頁碼.269-315

02/2022

DOI: https://doi.org/10.1016/j.jnt.2021.05.002

摘要

Special values of L-functions

Whittaker periods for GL3

Algebra and Number Theory

Let Π be a cohomological irreducible cuspidal automorphic representation of GL ₂ (A _F ) with central character ω _Π 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 ω _Π ⁻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 Sym ² Π of Π.

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題名: Algebraicity of the near central non-critical values of symmetric fourth L-functions for Hilbert modular forms
翻譯題名: Algebraicity of the near central non-critical values of symmetric fourth L-functions for Hilbert modular forms
創作者：: Shih-Yu Chen (作者) - Institute of Mathematics, Academia Sinica
學術資源類型: 期刊文章
出版日期: 02/2022
出版資訊: Journal of Number Theory, 卷.231, 頁碼.269-315
語言: 英語

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

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