This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Papers following peer review. The definitive publisher-authenticated version in Int Math Res Papers (2006) Vol. 2006, article ID 68213 is available online at doi:10.1155/IMRP/2006/68213.


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.