標題: 伽羅瓦表現與模型式
Galois Representations and Modular Forms
作者: 黃彥璋
Huang, Yan-Jhang
楊一帆
Yang, Yi-Fan
應用數學系所
關鍵字: 伽羅瓦;表現式;模型式;Galois;representation;Modular form
公開日期: 2009
摘要: 我們想要探討的問題,是如何去尋找一個簡單的方法來討論一個特別的函數x4-2在模掉一個質數p之後解的個數。這是一個跟Hecke L-函數、伽羅瓦群、群的表現有關的應用問題。 更進一步來說,我們可利用這個多項式解空間的伽羅瓦表現來找出一個weight為12,level為256的cusp form。
The problem we want to discuss in this thesis is trying to find a simple description “How the polynomial splits modulo a prime p for a special polynomial x4-2.” This is an application of Hecke L-function, the Galois theorem and the group representation. We will try to connect them by some well-known knowledge, and use them to solve the problem in our discussion. Moreover, we will use the Galois representation of the splitting filed of the polynomial x4-2 to construct a cusp form of weight 1 with level 256.
URI: http://140.113.39.130/cdrfb3/record/nctu/#GT079722515
http://hdl.handle.net/11536/45069
Appears in Collections:Thesis