標題: | 志村曲線之定義方程式 Equations of Shimura Curves |
作者: | 施建宏 Shih, Chien-Hung 楊一帆 Yang, Yi-Fan 應用數學系所 |
關鍵字: | 志村曲線;Shimura Curves |
公開日期: | 2012 |
摘要: | 在這篇論文中,我們會討論在給定不同D值下的志村曲線的方程式,這裡$W_D$代表所有在$X^D_0(1)$上的Atkin-Lehner involutions所形成的群。論文中最主要的想法是建構兩個合適且weight為0的Borcherds form以產生在$X^D_0(1)$模函數組成的體,藉由Schofer的方程式來計算不同Borcherds form在CM點上的值最後找出兩個Borcherds form的關聯性。 In the thesis, we will determine the equations of Shimura curves$X^D_0(1)/W_D$ of genus one for several D, where $W_D$ denotes the group of all Atkin-Lehner involutions on $X^D_0(1)$. The main idea is to construct two suitable Borcherds forms of weight 0 that generate the field of modular functions on $X^D_0(1)/W_D$ and use Schofer’s formula for values of Borcherds forms at CM-points to find the relation between the two Borcherds forms. |
URI: | http://140.113.39.130/cdrfb3/record/nctu/#GT079822511 http://hdl.handle.net/11536/73166 |
顯示於類別: | 畢業論文 |