#### Vol. 306, No. 1, 2020

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Bergman kernels of elementary Reinhardt domains

### Debraj Chakrabarti, Austin Konkel, Meera Mainkar and Evan Miller

Vol. 306 (2020), No. 1, 67–93
##### Abstract

We study the Bergman kernel of certain domains in ${ℂ}^{n}$, 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.

Bergman kernel
Primary: 32A25
Secondary: 32A07