Lifting for Siegel modular forms of half-integral weight

模形式是复数变量的函数，有很好的变换公式。所谓的“提升”是若干变量的模形式空间之间的某些映射，“提升”对于研究模形式空间的结构和l函数的性质是有用的。本文在构造形式不消失的假设下，得到了两种椭圆模形式到偶数次半积分权的西格尔模形式的提升映射。为了证明这种提升性，我对偶次半积分权的西格尔模形式的质量关系进行了一定的推广。

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.