On the adjoint L-function of the p-adic GSp(4)

We explicitly compute the adjoint L-function of those L-packets of representations of the group GSp(4) over a p-adic field of characteristic zero that contain non-supercuspidal representations. As an application we verify a conjecture of Gross and Prasad and Rallis in this case. The conjecture states that the adjoint L-function is holomorphic at s=1 if and only if the L-packet contains a generic representation.