Galois Representations and Modular Forms

• Main Authors: Ting-Han Huang, 黃庭瀚
• Other Authors: 于靖
• Format: Others
• Language: zh-TW
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/ynd525

碩士 === 國立臺灣大學 === 數學研究所 === 106 === In this thesis, I briefly give an introduction to the relation between Galois representations and modular forms, especially the modular forms of weight one. A main source is the paper “Formes modulaires de poid 1” written by Deligne and Serre in 1974. In section 2, we first state some required knowledge of modular forms and Galois representations. In section 3 and 4, we give an outline of the original proof of Deligne and Serre and make some remarks. The first part of the appendix part contains a short introduction of Wiles’ work, which concerns the weight two case. The rest part of the appendix contains some computations and proof of several results mentioned in section 2, so that the thesis is more self-contained.