Survey Article: Characterizations of the Saito-Kurokawa Lifting

David W. Farmer
Ameya Pitale
Nathan C. Ryan, Bucknell University
Ralf Schmidt


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.