We show a relation between a certain period and the existence of a simple pole for the spin and standard partial L functions corresponding to a generic cuspidal representation defined on the group GSO8(A). We also relate these two conditions with the functorial lift from the exceptional group G2 to GSO8. The main new ingridient is a new multivariable Rankin-Selberg integral which represents the above two L functions.
Ginzburg, David and Hundley, Joseph. "Multi-variable Rankin-Selberg Integrals for Orthogonal Groups." (Jan 2004).