Equations of Shimura Curves
碩士 === 國立交通大學 === 應用數學系所 === 101 === 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 tha...
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Format: | Others |
Language: | en_US |
Published: |
2013
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Online Access: | http://ndltd.ncl.edu.tw/handle/83958486170077279452 |
Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 101 === 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.
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