On L-factors attached to generic representations of unramified $$\mathrm {U}(2,1)$$ U ( 2 , 1 )

Abstract

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