# Gamma factors for the Asai cube representation

## TL;DR

This paper establishes an equality between gamma factors for the Asai cube representation and local zeta integrals, leading to new insights into the analytic properties of associated automorphic L-functions.

## Contribution

It proves the equality of gamma factors for the Asai cube representation using Weil-Deligne and local zeta integrals, advancing understanding of their analytic behavior.

## Key findings

- Gamma factors for Asai cube representation are equal to local zeta integrals.
- Derived analytic properties of automorphic L-functions for the Asai cube.
- Enhanced understanding of local-global compatibility in automorphic forms.

## Abstract

We prove an equality between the gamma factors for the Asai cube representation of ${\rm R}_{E/F}{\rm GL}_2$ defined by the Weil$-$Deligne representations and the local zeta integrals of Ikeda and Piatetski-Shapiro$-$Rallis, where $E$ is an \'etale cubic algebra over a local field $F$ of characteristic zero. As an application we obtain the analytic properties of the automorphic $L$-functions for the Asai cube representation.