An explicit inversion formula for the p-adic Whittaker transform on GL_n(ℚ_p)

2017/02/27 by João Guerreiro, Guerreiro, João
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Primary 11F85 #Secondary 22E35

paper · pdf · doi:10.48550/arxiv.1702.08271

openalex publication_date 2017/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Whittaker functions on non-archimedean fields were first introduced in the work of Jacquet, and they were characterized explicitly by Shintani. We obtain an explicit inversion formula and a Plancherel formula for the p-adic Whittaker transform on GL_n(ℚ_p). As an application, integral representations are obtained for the local factors of certain symmetric power L-functions.

Citations

• Formule de Plancherel pour les fonctions de Whittaker sur un groupe\n r 'eductif p-adique

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