The spin L-function of quasi-split D4

Abstract

We construct a multivariable Rankin-Selberg integral for the Spin L-function of a globally generic cuspidal representation of an arbitrary quasi-split group of type D4. This proves the meromorphic continuation of this L-function. When the quasi-split group of type D4 is associated to a cubic field extention, this L-function cannot be analyzed by the Langlands-Shahidi method.