A NOTE ON THE SAITO-KUROKAWA LIFT FOR HERMITIAN FORMS
The aim of this paper is to give a short proof of the Saito-Kurokawa lift for Hermitian modular forms along the lines we gave in an earlier paper [18]. The proof uses a converse theorem as was initially proven by Imai yet avoiding the framework of spectral analysis.
The proof heavily relies on the observation, that the partial Mellin transform of the Saito-Kurokawa lift of the cusp forms from Kojimas plus space coincides with a certain Siegel theta lift of f matched with a real analytic Eisenstein series. The functional equation of the Eisenstein series then implies the desired functional equation for the partial Mellin transform which in turn proves the lift to be a Hermitian modular form.
Saito-Kurokawa lift, Siegel theta series, Hermitian modular forms.