Bergman Kernels of Elementary Reinhardt Domains

Abstract

We study the Bergman kernel of certain domains in ${\mathbb{C}}^n$, called elementary Reinhardt domains, generalizing the classical Hartogs triangle. For some elementary Reinhardt domains, we explicitly compute the kernel, which is a rational function of the coordinates. For some other such domains, we show that the kernel is not a rational function. For a general elementary Reinhardt domain, we obtain a representation of the kernel as an infinite series.

Typos corrected. To appear in Pacific Journal of Mathematics

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