The Bergman kernel of a certain Hartogs domain and the polylogarithm function

2010/08/31 by Yamamori, Atsushi
#32A25 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1008.5339

Abstract

We consider a certain Hartogs domain which is related to the Fock-Bargmann space. We give an explicit formula for the Bergman kernel of the domain in terms of the polylogarithm functions. Moreover we solve the Lu Qi-Keng problem of the domain in some cases.

Related

• Zeros of the Bergman kernel of the Fock-Bargmann-Hartogs domain and the interlacing property
• Relationships Between the Bergman Kernels of Hartogs Domains and Their Base
• The Bergman Kernel on some Hartogs domains
• Some Topics Related to Bergman Kernel
• Weighted Bergman kernel functions associated to meromorphic functions