Bergman theory of certain generalized Hartogs triangles

Abstract: The Bergman theory of domains ${ |{z_{1} |^{\gamma}} < |{z_{2}} | < 1 }$ in $\mathbb{C}^2$ is studied for certain values of $\gamma$, including all positive integers. For such $\gamma$, we obtain a closed form expression for the Bergman kernel, $\mathbb{B}{\gamma}$. With these formulas, we make new observations relating to the Lu Qi-Keng problem and analyze the boundary behavior of $\mathbb{B}{\gamma}(z,z)$.