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

Preprint Series # 806
Katsurada, Hidenori and Kawamura, Hisa-aki A certain Dirichlet series of Rankin-Selberg type associated with the Ikeda lifting. (2006);

In this paper, we consider a certain Dirichlet series of Rankin-Selberg type associated with two Siegel cusp forms with respect to $Sp_n(\bf Z)$, which can be viewed as a generalization of the Rankin-Selberg convolution series for two elliptic modular forms. In particular, we give the explicit formula for the Dirichlet series associated with the so-called Ikeda lifting of cuspidal Hecke eigenforms with respect to $SL_2(\bf Z)$. We also comment on a contribution to the Ikeda's conjecture on periods of the lifting.