Modular descent of Siegel modular forms of half integral weight and an analogy of the Maass relation

Abstract

In [8], H. Maass introduced the ‘Spezialschar’ which is now called the Maass space. It is defined by the relation of the Fourier coefficients of modular forms as follows. Let f be a Siegel modular form on Sp(2,Z) of weight k, and let be its Fourier expansion, where . Then f belongs to the Maass space if and only if