Lifting from two Elliptic Modular Forms to Siegel Modular Forms of Half-Integral Weight of even Degree

The aim of this paper is to construct lifts from two elliptic modular forms to Siegel modular forms of half-integral weight of even degree under the assumption that the constructed Siegel modular form is not identically zero. The key ingredient of the proof is a new Maass relation for Siegel modular forms of half-integral weight and any degree.

2010 Mathematics Subject Classification: 11F46 (primary), 11F37, 11F50 (secondary)

Keywords and Phrases: Siegel modular forms, Jacobi forms, Maass relation

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