On epsilon factors attached to supercuspidal representations of unramified $\mathrm {U}(2,1)$
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Abstract:
Let $G$ be the unramified unitary group in three variables defined over a $p$-adic field $F$ with $p \neq 2$. 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 $G$.References
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Additional Information
- Michitaka Miyauchi
- Affiliation: Faculty of Liberal Arts and Sciences, Osaka Prefecture University, 1-1 Gakuen-cho Nakaku Sakai, Osaka 599-8531, Japan
- Email: michitaka.miyauchi@gmail.com
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 3355-3372
- MSC (2010): Primary 22E50, 22E35
- DOI: https://doi.org/10.1090/S0002-9947-2013-05859-X
- MathSciNet review: 3034469