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

Abstract

We consider a certain Dirichlet series of Rankin–Selberg type associated with two Siegel cusp forms of the same integral weight with respect to Sp n ( Z ) . In particular, we give an explicit formula for the Dirichlet series associated with the Ikeda lifting of cuspidal Hecke eigenforms with respect to SL 2 ( Z ) . We also comment on a contribution to the Ikeda's conjecture on the period of the lifting.