The zeros of theta functions belonging to binary-Hermitian forms over \(\mathbb{Z}[i]\)
We determine the zeros of the theta functions (defined and holomorphic on the upper halfplane) \(\theta(z)= \sum_{x,y\in\mathbb{Z}[i]} e^{\pi i{\mathbf Q}(x,y)z}\), and of related functions, \(Q\) any positive binary-Hermitian form over \(\mathbb{Z}[i]\). In particular we show that all these zeros are Heegner-points.
scientific article; zbMATH DE number 567449