The exterior cube L-function for GL(6)

We construct a Rankin Selberg integral to represent the exterior cube L fun ction L(pi,Lambda (3),s) of an automorphic cuspidal module pi of GL(6)(A(F) ) (where F is a number field). We determine the poles of this L function an d find period conditions for the special value L(pi,Lambda (3),1/2). We use the Siegal Weil formula. We also state an analogue of the Gross-Prasad con jecture concerning a criterion for the nonvanishing of L(pi,Lambda (3),1/2) .