Abstract
We consider the Reinhardt domainDn={(ζ,z)∈C×Cn:|ζ|2<(1-|z1|2)⋯(1-|zn|2)}.We express the explicit closed form of the Bergman kernel forDnusing the exponential generating function for the Stirling number of the second kind. As an application, we show that the Bergman kernelKnforDnhas zeros if and only ifn≥3. The study of the zeros ofKnis reduced to some real polynomial with coefficients which are related to Bernoulli numbers. This result is a complete characterization of the existence of zeros of the Bergman kernel forDnfor all positive integersn.
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