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.
"Weighted Bergman kernel functions associated to meromorphic functions." Rocky Mountain J. Math. 47 (1) 239 - 257, 2017. https://doi.org/10.1216/RMJ-2017-47-1-239