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

TL;DR

This paper develops a newform theory for unramified U(2,1) representations, linking zeta integrals to L and epsilon-factors, and providing explicit formulas for these factors in the context of Rankin-Selberg integrals.

Contribution

It introduces a newform framework for the Rankin-Selberg integral on unramified U(2,1), connecting zeta integrals with L and epsilon-factors, and deriving explicit formulas.

Findings

Zeta integrals of newforms match L-factors.

Explicit formulas for epsilon-factors of generic representations.

Established a theory of newforms for the Rankin-Selberg integral.

Abstract

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.