The Zeros of the Bergman Kernel for Some Reinhardt Domains

We consider the reinhardt domain d n = { (ζ,z) c × c n: | ζ | 2 < (1 - | z 1 | 2) (1 - | z n | 2) }. we express the explicit closed form of the bergman kernel for d n using the exponential generating function for the stirling number of the second kind. as an application,we show that the bergman kernel k n for d n has zeros if and only if n ≥ 3. the study of the zeros of k n is reduced to some real polynomial with coefficients which are related to bernoulli numbers. this result is a complete characterization of the existence of zeros of the bergman kernel for d n for all positive integers n. © 2016 jong-do park.