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

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Abstract

Let G be the unramified unitary group in three variables defined over a p-adic field with p≠ 2. 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 ε-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 ε-factors of generic representations.

Original languageEnglish
Pages (from-to)1381-1408
Number of pages28
JournalMathematische Zeitschrift
Volume289
Issue number3-4
DOIs
Publication statusPublished - Aug 1 2018

Keywords

  • L-factor
  • Local newform
  • p-adic group

ASJC Scopus subject areas

  • Mathematics(all)

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