On the Miyawaki lifts of hermitian modular forms

We construct a lifting from an elliptic modular cusp form f and a hermitian modular cusp form g of degree r to a hermitian modular cusp form of degree n+r. This lift is the so-called Miyawaki lift. When f and g are “Hecke eigenforms”, its lift is also a “Hecke eigenform” (if it is not identically zero). Moreover, we determine explicitly the standard L-function and the A-parameter associated to the Miyawaki lift.