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∈C3:|z1|2+|z2|q<1,|z1|2+|z3|r<1}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{z \in \mathbb {C}^3 :|z_1|^2 + |z_2|^q < 1, |z_1|^2 + |z_3|^r < 1\}$$\end{document}.