Lu Qi-Keng Problem and Topological Properties of Zero Variety on the Thullen Domain

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 po such that the Bergman kernel function has zero points for 0 < p < po. 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.