Vol. 306, No. 1, 2020

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Bergman kernels of elementary Reinhardt domains

Debraj Chakrabarti, Austin Konkel, Meera Mainkar and Evan Miller

Vol. 306 (2020), No. 1, 67–93
Abstract

We study the Bergman kernel of certain domains in n, called elementary Reinhardt domains, generalizing the classical Hartogs triangle. For some elementary Reinhardt domains, we explicitly compute the kernel, which is a rational function of the coordinates. For some other such domains, we show that the kernel is not a rational function. For a general elementary Reinhardt domain, we obtain a representation of the kernel as an infinite series.

Keywords
Bergman kernel
Mathematical Subject Classification 2010
Primary: 32A25
Secondary: 32A07
Milestones
Received: 6 September 2019
Revised: 3 January 2020
Accepted: 12 January 2020
Published: 14 June 2020
Authors
Debraj Chakrabarti
Department of Mathematics
Central Michigan University
Mt Pleasant, MI
United States
Austin Konkel
Department of Mathematics
Central Michigan University
Mt Pleasant, MI
United States
Meera Mainkar
Department of Mathematics
Central Michigan University
Mt Pleasant, MI
United States
Evan Miller
Department of Mathematics
Central Michigan University
Mt Pleasant, MI
United States