Weighted Bergman kernel functions associated to meromorphic functions

Robert Jacobson, Roger Williams University

Document Type Article

Abstract

We present a technique for computing explicit, concrete formulas for the weighted Bergman kernel on a planar domain with modulus squared weight of a meromorphic function in the case that the meromorphic function has a finite number of zeros on the domain and a concrete formula for the unweighted kernel is known. We apply this theory to the study of the Lu Qi-keng problem.