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

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.

6pages

References in corpus (1)

• Polynômes de Hua, noyau de Bergman des domaines de Cartan-Hartogs et problème de Lu Qikeng

Cited by in corpus (1)

• Zeros of the Bergman kernel of the Fock-Bargmann-Hartogs domain and the interlacing property