Algebraicity of the near central non-critical values of symmetric fourth L-functions for Hilbert modular forms
| Autor: | Shih-Yu Chen |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Statistics::Theory
Pure mathematics Algebra and Number Theory Non critical Mathematics - Number Theory Statistics::Applications Degree (graph theory) Mathematics::Number Theory Modular form Lift (mathematics) Character (mathematics) Norm (mathematics) FOS: Mathematics Number Theory (math.NT) Totally real number field Mathematics::Representation Theory Representation (mathematics) Mathematics |
| Zdroj: | Journal of Number Theory. 231:269-315 |
| ISSN: | 0022-314X |
| Popis: | Let $\mathit{\Pi}$ be a cohomological irreducible cuspidal automorphic representation of ${\rm GL}_2(\mathbb{A}_{\mathbb F})$ with central character $\omega_{\mathit{\Pi}}$ 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 $\mathit{\Pi}$ twisted by $\omega_{\mathit{\Pi}}^{-2}$. The algebraicity is expressed in terms of the Petersson norm of the normalized newform of $\mathit{\Pi}$ and the top degree Whittaker period of the Gelbart-Jacquet lift ${\rm Sym}^2\mathit{\Pi}$ of $\mathit{\Pi}$. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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