本文研究緊緻Kähler 流形之覆蓋流形上的Bergman 核漸近展開。在回顧緊緻情 形下的局部縮放論證與逐點漸近展開後，我們將幾何結構提升至一個Galois覆蓋流形 上。 利用Bergman 核展開的局部性，我們得到覆蓋流形上L²-Bergman 核的相應漸近 行為，並推導出L²-全純截面空間之Γ-維度的首項漸近公式。;This thesis studies Bergman kernel asymptotics on covering manifolds of compact Kähler manifolds. After reviewing the local scaling argument and the pointwise asymptotic expansion in the compact case， we lift the geometric setting to a Galois covering manifold. Using the locality of the Bergman kernel expansion， we obtain the corresponding asymptotic behavior of the L2-Bergman kernel on the covering manifold and derive the leading asymptotic formula for the Γ-dimension of the space of L2-holomorphic sections.
