The Exterior Cube L-Function for GL(6)

Abstract

We construct a Rankin Selberg integral to represent the exterior cube L function L(π, Λ3, s) of an automorphic cuspidal module π of GL6(double-struck AF) (where F is a number field). We determine the poles of this L function and find period conditions for the special value L(π, Λ3, 1/2). We use the Siegal Weil formula. We also state an analogue of the Gross-Prasad conjecture concerning a criterion for the nonvanishing of L(π, Λ3, 1/2).