Lifting for Siegel modular forms of half-integral weight

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Modular forms are functions of complex variables which have nice transformation formula. So-called "liftings" are certain maps between the space of modular forms of several variables and "liftings" are useful to investigate the structure of the space of modular forms and the properties of the L-functions.In this study I obtained lifting maps from two elliptic modular forms to Siegel modular forms of half-integral weight of even degrees under the assumption that the constructed form does not vanish. To show the lifting I obtained a certain generalization of the Maass relation for Siegel modular forms of half-integral weight of even degrees.