On Petersson norms of generic cusp forms and special values of adjoint L-functions for GSp(4)

We prove an explicit formula for the Petersson norms of some normalized generic cuspidal newforms on GSp ₄ whose archimedean components belong to either discrete series representations or spherical principal series representations. Our formula expresses the Petersson norms in terms of special values of adjoint L-functions and some elementary constants depending only on local repre-sentations.