Characterizations of the Saito-Kurokawa lifting: a survey
David W. Farmer, Ameya Pitale, Nathan C. Ryan, and Ralf Schmidt
TL;DR
This survey reviews various known characterizations of Saito-Kurokawa lifts and introduces new, simpler characterizations using recent results, enhancing understanding of these lifts in modular form theory.
Contribution
The paper compiles existing characterizations and introduces novel, simplified criteria for identifying Saito-Kurokawa lifts based on Weissauer's recent findings.
Findings
New simpler characterizations of Saito-Kurokawa lifts
Application of Weissauer's recent result to modular forms
Comprehensive survey of known characterizations
Abstract
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.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Geometry and complex manifolds