论文标题
对称对称的第四$ L $ formartions Hilbert模块化形式的近乎中心非关键价值的代数
Algebraicity of the near central non-critical value of symmetric fourth $L$-functions for Hilbert modular forms
论文作者
论文摘要
令$ \mathitπ$为$ {\ rm gl} _2（\ Mathbb {a} _ {\ Mathbb f}）$的共同学不可记录的cuspidal自动形态表示，带有中心字符$ $ω_ {\mathitπ} $，而不是完全真实的数字字段$ {在本文中，我们证明了$ \mathitπ$ twist twist twist twist twist twist twist twist twist twist twist twist twist twist twist的对称的第四$ l $ function的代数。代数是根据$ \Mathitπ$的归一化新形式和Gelbart-Jacquet Lift $ {\ rm sym}^2 \Mathitπ$的$ \ \Mathitπ$表示的。
Let $\mathitΠ$ be a cohomological irreducible cuspidal automorphic representation of ${\rm GL}_2(\mathbb{A}_{\mathbb F})$ with central character $ω_{\mathitΠ}$ over a totally real number field ${\mathbb F}$. In this paper, we prove the algebraicity of the near central non-critical value of the symmetric fourth $L$-function of $\mathitΠ$ twisted by $ω_{\mathitΠ}^{-2}$. The algebraicity is expressed in terms of the Petersson norm of the normalized newform of $\mathitΠ$ and the top degree Whittaker period of the Gelbart-Jacquet lift ${\rm Sym}^2\mathitΠ$ of $\mathitΠ$.
