Jacobi Forms of Several Variables and the Maaß Space Original Research Article

In this paper we describe the space of Jacobi forms on image×imagen. This type of Jacobi forms appears in the Fourier–Jacobi expansions of all kinds of modular forms of several variables. We can characterize the space of Jacobi forms of weightkby vector valued elliptic modular forms of weightk−n/2. Then we use the Jordan theoretic language in order to describe modular forms on the orthogonal groupO(2, n+2), whose Fourier–Jacobi expansions also yield Jacobi forms of our type. Finally we determine a Maaß space as the isomorphic image of a particular space of Jacobi forms. Especially our procedure guarantees the existence of certain non-trivial singular modular forms.