Derives explicit formulas for Bergman kernels in cylindrical domains, suggesting broader applications in complex analysis.
In 2016, Beberok obtained an explicit formula for the Bergman kernel of a specific Reinhardt domain in ℂ3, defined by |ζ1|2<(1−|z|2)q,|ζ2|2<(1−|z|2)r where q,r>0. We derive explicit formulas for the Bergman kernels of a wider class of domains, expressed in terms of polylogarithm functions. This class includes Beberok's domain as a special case.
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Atsushi Yamamori (2026) studied this question.
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