On liftings of holomorphic modular forms

In this article, we discuss a lifting of elliptic cusp forms to higher dimensional symmetric spaces. We will consider two cases. The first case is the Siegel modular case, and the second case is the hermitian modular case. The Fourier coefficients of our liftings are closely related to those of Eisenstein series. When the degree is 2, our lifting reduces to the classical Saito-Kurokawa lifting or hermitian Maass lifting.