  Let G be the unramified unitary group in three variables defined over a
p-adic field of odd residual characteristic. 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 epsilon-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 epsilon-factors of generic representations.
