The Bergman kernel function for intersections of some cylindrical domains and Lauricella's hypergeometric function

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Abstract

In this paper, we show that Lauricella's hypergeometric function F8 has a close connection with the Bergman kernel for the intersection of two cylindrical domains defined by D(p1,p2,p3):={z∈C3:|z1|2p1+|z2|2p2<1,|z1|2p1+|z3|2p3<1}. We investigate the boundary behavior of the Bergman kernel on the diagonal (z1,0,0). We also compute the explicit form of the Bergman kernel when (p1,p2,p3)=(1,p2,p3) and (p,1,1). As a consequence, we show that D(1,p2,p3) is a Lu Qi-Keng domain. All results can be generalized to the intersection of cylindrical domains in any higher dimension.

Original languageEnglish
Article number125398
JournalJournal of Mathematical Analysis and Applications
Volume504
Issue number1
DOIs
Publication statusPublished - 1 Dec 2021

Keywords

  • Bergman kernel
  • Gauss hypergeometric function
  • Lauricella's function
  • Lu Qi-Keng problem

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