我們參考Kubert和Lang的做法，以Stickelberger分佈去分析Drinfeld-Siegel可逆模函數在Drinfeld模曲線尖點處的零根數。我們證明在給定的等級下Drinfeld-Siegel可逆模函數能夠生成出對於所有Drinfeld可逆模函數的一個有限指數子群，並且能推論出對於Drinfeld模曲線的Picard群中尖點因子子群的有限性。

We follow Kubert and Lang's method on Stickelberger distribution to analyze the orders of vanishing of Drinfeld-Siegel units at cusps of Drinfeld modular curves. Our result shows that for a given level, the Drinfeld-Siegel units generate a finite index subgroup of all Drinfeld modular units. A direct consequence is the finiteness of the cuspidal divisor subgroup of the Picard group of a Drinfeld modular curve.

Abstract
誌謝辭
Contents
Chapter 1. Introduction----------------------------------------1
Chapter 2. The Cartan Groups-----------------------------------5
Chapter 3. Distributions---------------------------------------7
3.1. Stickelberger Distributions-------------------------------8
3.2. Bernoulli Distributions----------------------------------10
3.3. Hurwitz Zeta Function------------------------------------12
Chapter 4. Drinfeld Modular Units-----------------------------17
4.1. Drinfeld Modular Forms-----------------------------------17
4.2. Klein Forms----------------------------------------------19
4.3. Drinfeld Modular Units and Cusps-------------------------21
4.4. Drinfeld-Siegel Units------------------------------------24
4.5. Examples of Indices--------------------------------------26
4.6. Drinfeld Modular Curves and Cuspidal Divisor Subgroups---27
Appendix A. Code----------------------------------------------29
List of Symbols-----------------------------------------------31
Bibliography--------------------------------------------------33

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