Lu Qi-Keng's problem for intersection of two complex ellipsoids

In this paper We investigate the Lu Qi-Keng problem for intersection of two complex ellipsoids \{z \in \mathbb{C}^3 \colon |z_1|^2 + |z_2|^q < 1, \quad |z_1|^2 + |z_3|^r < 1\}.