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The Bergman kernel for intersection of two complex ellipsoids

Tomasz Beberok
대한수학회 (The Korean Mathematical Society)|2016.09|대한수학회보 (Bulletin of the KMS)|제53권 제5호|pp. 1291-1308

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참고문헌

키워드

hypergeometric functionsBergman kernelLu Qi-Keng problem
주제분류수학

초록

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 $\{z \in \mathbb{C}^3 \colon |z_1|^p + |z_2|^q < 1$, $|z_1|^p + |z_3|^r < 1\}$. We consider cases $p=6$, $q= r= 2$ and $p=q=r=2$. We also investigate the Lu Qi-Keng problem for $p=q=r=2$.

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 $\{z \in \mathbb{C}^3 \colon |z_1|^p + |z_2|^q < 1$, $|z_1|^p + |z_3|^r < 1\}$. We consider cases $p=6$, $q= r= 2$ and $p=q=r=2$. We also investigate the Lu Qi-Keng problem for $p=q=r=2$.

참고문헌 (23)

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