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arXiv · 1507.06150

The Bergman kernel for intersection of two complex ellipsoids

Tomasz Beberok
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Abstract

In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for intersection of two complex ellipsoids $\{z \in \mathbb{C}^3 \colon |z_1|^p + |z_2|^q < 1, \quad |z_1|^p + |z_3|^r < 1\}$. We consider cases $p=6, q= r= 2$ and $p=q=r=2$. We also investigate the Lu Qi-Keng problem for $p=q=r=2$.

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Tomasz Beberok. 2015-07-22. The Bergman kernel for intersection of two complex ellipsoids. https://arxiv.org/abs/1507.06150

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