On epsilon factors attached to supercuspidal 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 F with p ≠ 2. Gelbart, Piatetski-Shapiro and Baruch attached zeta integrals of Rankin-Selberg type to irreducible generic representations of G. In this paper, we formulate a conjecture on L- and ε-factors defined through zeta integrals in terms of newforms for G, which is an analogue of the result by Casselman and Deligne for GL(2). We prove our conjecture for the generic supercuspidal representations of G.

Original languageEnglish
Pages (from-to)3355-3372
Number of pages18
JournalTransactions of the American Mathematical Society
Volume365
Issue number6
DOIs
Publication statusPublished - 2013
Externally publishedYes

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P-adic Fields
Unitary group
Analogue

Keywords

  • ε-factor
  • Local newform
  • P-adic group

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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abstract = "Let G be the unramified unitary group in three variables defined over a p-adic field F with p ≠ 2. Gelbart, Piatetski-Shapiro and Baruch attached zeta integrals of Rankin-Selberg type to irreducible generic representations of G. In this paper, we formulate a conjecture on L- and ε-factors defined through zeta integrals in terms of newforms for G, which is an analogue of the result by Casselman and Deligne for GL(2). We prove our conjecture for the generic supercuspidal representations of G.",
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AB - Let G be the unramified unitary group in three variables defined over a p-adic field F with p ≠ 2. Gelbart, Piatetski-Shapiro and Baruch attached zeta integrals of Rankin-Selberg type to irreducible generic representations of G. In this paper, we formulate a conjecture on L- and ε-factors defined through zeta integrals in terms of newforms for G, which is an analogue of the result by Casselman and Deligne for GL(2). We prove our conjecture for the generic supercuspidal representations of G.

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