Some Remarks on the Saito Kurokawa Lift for Orthogonal Forms

Abstract

Duke and Imamoglu showed that the Saito–Kurokawa lift for Siegel modular forms can in an elegant manner be obtained from a converse theorem by Imai using spectral analysis of the hyperbolic Laplacian. In an earlier paper we gave a simplified approach without any appeal to spectral analysis. Here we want to show, that this generalizes to some orthogonal groups of signature (2,m+2) with m>2.