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研究生： 何盛揚
Ho, Sheng-Yang
論文名稱： 德林費爾德模上的邦別里-瓦勒-馬瑟理論
A Bombieri-Vaaler-Masser Theorem for Drinfeld Modules
指導教授： 張介玉
Chang, Chieh-Yu
口試委員: 于靖
Yu, Jing
魏福村
Wei, Fu-Tsun
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2020
畢業學年度： 108
語文別： 英文
論文頁數： 22
中文關鍵詞： 德林費爾德模 、邦別里-瓦勒理論 、馬瑟理論 、演算法
外文關鍵詞： Drinfeld Modules, Bombieri-Vaaler Theorem, Masser's Theorem, Algorithm
相關次數： 點閱：2  下載：0 
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    • 摘要：在本論文中，我們研究一個在德林費爾德模上的邦別里-瓦勒-馬瑟理論問
    題。我們建立了一種演算法來計算在基本多項式環上定義的德林費爾德模上，由有
    限多個整數點所生成的子模的秩。在附錄中，我們利用SageMath提供了計算結果和
    程式碼。

    In this thesis, we study a problem of Bombieri-Vaaler-Masser theorem for Drinfeld modules. We establish an effective algorithm to compute the rank of the submodule generated by a finite set of integral points of a Drinfeld module defined over the base polynomial ring. In the appendix, we provide computational results and the programming code in SageMath.

    Declaration of Authorship i Abstract ii Acknowledgements iii 1 Notation and Introduction 1 1.1 Introduction 1 1.2 Notation 2 1.3 Main theorem 2 1.4 Outline of the proof of main theorem 3 2 Preliminaries 5 2.1 Anderson t-motives and Ext modules 5 2.2 Drinfeld modules and their associated Frobenius modules 9 3 The main result 12 3.1 Main theorem 12 3.2 The algorithm 15 3.3 Time complexity 16 A Code and Examples 17 A.1 Code 17 A.2 Examples 20

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