Gamma factors for Asai representations of \rm GL₂

2018/10/30 by Shih-Yu Chen, Yao Cheng, Chen, Shih-Yu +4 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1810.12561

arxiv created 2018/10/30 · openalex publication_date 2018/10/30 · arxiv updated 2018/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let E be a quadratic semisimple extension of a local field F of characteristic zero. We determine explicit relation between gamma factors for Asai representations of R_E/F\rm GL_2/E defined by the Weil-Deligne representations and local zeta integrals. When E = F× F, the results were due to Henniart and Jacquet. We completed the theory in this article based on explicit calculation.

Citations

• Fourier Transforms of Intertwining Operators and Plancherel Measures for GL(n)
• Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique
• Rankin-Selberg Convolutions

Cited by

• Archimedean theory and ε-factors for the Asai Rankin-Selberg integrals

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