On epsilon factors attached to supercuspidal representations of unramified 𝑈(2,1)

Miyauchi, Michitaka

doi:10.1090/S0002-9947-2013-05859-X

On epsilon factors attached to supercuspidal representations of unramified $\mathrm {U}(2,1)$
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Trans. Amer. Math. Soc. 365 (2013), 3355-3372 Request permission

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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