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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On epsilon factors attached to supercuspidal representations of unramified $ \mathrm{U}(2,1)$

Author: Michitaka Miyauchi
Journal: Trans. Amer. Math. Soc. 365 (2013), 3355-3372
MSC (2010): Primary 22E50, 22E35
Published electronically: January 4, 2013
MathSciNet review: 3034469
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Abstract: Let $ G$ be the unramified unitary group in three variables defined over a $ p$-adic field $ F$ with $ p \neq 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 $ \varepsilon $-factors defined through zeta integrals in terms of newforms for $ G$, which is an analogue of the result by Casselman and Deligne for $ \mathrm {GL}(2)$. We prove our conjecture for the generic supercuspidal representations of $ G$.

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Michitaka Miyauchi
Affiliation: Faculty of Liberal Arts and Sciences, Osaka Prefecture University, 1-1 Gakuen-cho Nakaku Sakai, Osaka 599-8531, Japan

Keywords: $p$-adic group, local newform, $𝜖$-factor
Received by editor(s): August 1, 2011
Received by editor(s) in revised form: March 23, 2012, and April 16, 2012
Published electronically: January 4, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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