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 p≠ 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 ε-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 ε-factors of generic representations.