We investigate Siegel theta series for quadratic forms of signature (m−1,1). On the one hand, we construct a holomorphic that does not transform like modular form. other non-holomorphic transforms form weight m/2. Moreover, describes almost everywhere part series.

We explore the consequences of the structure of the discrete automorphic spectrum of the split orthogonal group SO(5) for holomorphic Siegel modular forms of degree 2. In particular, the combination of the local and global packet structure with the local paramodular newform theory for GSp(4) leads to a strong multiplicity one theorem for paramodular cusp forms.