The main purpose of this paper
is to give the affirmative solution for the Lu Qi-Keng conjecture in the case of
bounded complete circular domains.
Some results are that Bell’s proposition, which is related to the evaluation about
the Bergman kernel functions of homogeneous complete circular domains, is extended
to the case of bounded complete circular domains and that the Bergman
representative functions with respect to z0(≠0) of any bounded and any
homogeneous bounded complete circular domain with center at the origin
are biholomorphic and isomorphic (biholomorphic in the narrow sense),
respectively.
