This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The definitive publisher-authenticated version International Mathematics Research Notices (2004), #58, 3097-3119, is available online at doi: 10.1155/S1073792804141020.


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.