Siegel theta series for quadratic forms of signature (m-1, 1)

We investigate Siegel theta series for quadratic forms of signature (m - 1, 1). On the one hand, we construct a holomorphic series that does not transform like a modular form. On the other hand, we construct a non-holomorphic series that transforms like a Siegel modular form of weight m/2. Moreover, the holomorphic series describes almost everywhere the holomorphic part of the modular series. & COPY; 2023 Published by Elsevier Inc.