The Bergman kernel function: Explicit formulas and zeroes Academic Article

We show how to compute the Bergman kernel functions of some special domains in a simple way. As an application of the explicit formulas, we show that the Bergman kernel functions of some convex domains, for instance the domain in C 3 mathbb {C}^3 defined by the inequality | z 1 | + | z 2 | + | z 3 | > 1 |z_1|+|z_2|+|z_3|>1 , have zeroes.