The zeros of the Bergman kernel for some Reinhardt domains (Q340941)

Consider the Reinhardt domain NEWLINE\[NEWLINE D_n=\Big\{(\zeta,z_1,\dots,z_n)\in\mathbb C^{n+1}:|\zeta|^2<\prod_{j=1}^n(1-|z_j|^2)\Big\}. NEWLINE\]NEWLINE The author obtains an explicit closed form of the Bergman kernel of the domain \(D_n\). As an application, he shows that the Bergman kernel of the domain \(D_n\) has zeros if and only if \(n\geq 3\).