A certain Dirichlet series of Rankin–Selberg type associated with the Ikeda lifting

We consider a certain Dirichlet series of Rankin–Selberg type associated with two Siegel cusp forms of the same integral weight with respect to Spn(Z). In particular, we give an explicit formula for the Dirichlet series associated with the Ikeda lifting of cuspidal Hecke eigenforms with respect to SL2(Z). We also comment on a contribution to the Ikeda's conjecture on the period of the lifting.