论文标题
szego内核的无限产品表示
Infinite Product Representation for the Szego Kernel for an Annulus
论文作者
论文摘要
Szego内核在共形映射中有许多应用程序，并满足Kerzman-Stein积分方程。环的szego内核可以表示为双侧系列。在本文中，我们通过应用Ramanujan的总和来展示如何代表szego内核作为基本的双边系列和无限的产品表示。无限产物显然表现出Szego内核的零。还介绍了它与基本伽马函数和修改的jacobi theta函数的联系。结果扩展到Szego内核，用于一般环和加权的Szego内核。还介绍了基于双边序列和无限产物计算szego内核的数值比较。
The Szego kernel has many applications to problems in conformal mapping and satisfies the Kerzman-Stein integral equation. The Szego kernel for an annulus can be expressed as a bilateral series. In this paper, we show how to represent the Szego kernel for an annulus as a basic bilateral series and an infinite product representation through the application of the Ramanujan's sum. The infinite product clearly exhibits the zero of the Szego kernel for an annulus. Its connection with basic gamma function and modified Jacobi theta function is also presented. The results are extended to the Szego kernel for general annulus and weighted Szego kernel. Numerical comparisons on computing the Szego kernel for an annulus based on the bilateral series and the infinite product are also presented.
