Survey article: Characterizations of the Saito-Kurokawa lifting
Rocky Mountain Journal of Mathematics
There are a variety of characterizations of Saito-Kurokawa lifts from elliptic modular forms to Siegel modular forms of degree 2. In addition to giving a survey of known characterizations, we apply a recent result of Weissauer to provide a number of new and simpler characterizations of Saito-Kurokawa lifts.
Ryan, Nathan C.; Farmer, David W.; Pitale, Ameya; and Schmidt, Ralf. "Survey article: Characterizations of the Saito-Kurokawa lifting." Rocky Mountain Journal of Mathematics (2013) : 1747-1757.