On L-factors attached to generic representations of unramified U(2,1)

2012/08/01 by Michitaka Miyauchi, Miyauchi, Michitaka
Mathematics · #22E35 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:22E35 #msc:22E50

paper · pdf · doi:10.48550/arxiv.1208.0125

19 pages

arxiv created 2012/08/01 · openalex publication_date 2012/08/01 · arxiv updated 2012/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be the unramified unitary group in three variables defined over a p-adic field of odd residual characteristic. In this paper, we establish a theory of newforms for the Rankin-Selberg integral for G introduced by Gelbart and Piatetski-Shapiro. We describe L and epsilon-factors defined through zeta integrals in terms of newforms. We show that zeta integrals of newforms for generic representations attain L-factors. As a corollary, we get an explicit formula for epsilon-factors of generic representations.

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