Converse theorem for not necessarily cuspidal Siegel modular forms of degree 2 and Saito-Kurokawa lifting (Q2783761)

Imai studied a converse theorem for Siegel cusp forms of degree 2, which characterizes Siegel cusp forms of degree 2 with the functional equations satisfied by the corresponding Koecher-Maass series with Grössencharacters. Right after the appearance of her paper, Weissauer gave an extension to Siegel cusp forms of arbitrary degree. In this paper, the authors give a convenient converse theorem applicable to not necessarily cuspidal Siegel modular forms of degree 2, and moreover they apply it to a proof of the Saito-Kurokawa lifting for degree 2 including the case of Eisenstein series. The method is essentially based on that of Weissauer.