On L-factors attached to generic representations of unramified U(2,1)

Let G be the unramified unitary group in three variables defined over a p-adic field with (Formula presented.). 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 (Formula presented.)-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 (Formula presented.)-factors of generic representations.