Lu Qi-Keng problem and topological properties of zero variety on the Thullen domain. (English) Zbl 1527.32005
Summary: In this paper, we consider Lu Qi-Keng problem on the Thullen domain. By constructing an invariant, we find a self-reciprocal polynomial which depends only on the dimension and is independent of the parameter \(p\) of the Thullen domain, and then get a fixed number \(p_o\) such that the Bergman kernel function has zero points for \(0<p<p_o\). Meanwhile, when the Bergman kernel function has zeros, the topology of the zero variety and the set of boundary points which are the accumulation points of zeros are characterized.
MSC:
| 32A25 | Integral representations; canonical kernels (Szegő, Bergman, etc.) |
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