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Title: | 決定橢圓曲線上 L 函數的特殊零點 Determining the Special Zero of an L-function Associated to an Elliptic Curve |
Authors: | Chih-Kai Fang 方致凱 |
Advisor: | 陳其誠 |
Keyword: | 橢圓曲線,狄利克雷級數,模形式,赫克算子,模符號, elliptic curve,Dirichlet series,modular forms,Hecke operators,modular symbols, |
Publication Year : | 2019 |
Degree: | 碩士 |
Abstract: | 橢圓曲線的狄利克雷級數在 s=1 上的階是大家所感興趣的。Mazur、Tate 和
Teitelbaum 發現一個可以計算經扭變後的橢圓曲線的狄利克雷級數在特殊點 s=1 上 是否為零點的方法。這涉及到計算模符號。本篇論文主要內容是在於整理他們所給 出的方法後,同時提出一個完整的演算法列表計算出扭變後的橢圓曲線的狄利克 雷級數在特殊點 s=1 上是否為零點。 The order of the Dirichlet series of the elliptic curve at s=1 is of interest to everyone. Mazur, Tate, and Teitelbaum found a way to calculate whether the Dirichlet series of the twisted elliptic curve has a zero at the particular point s=1. This involves calculating the modulo symbol. The aim of this paper is to sort out the methods they have given, and at the same time propose a complete list of algorithms to calculate whether the Dirichlet series of the twisted elliptic curve has a zero at the special point s=1. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/71508 |
DOI: | 10.6342/NTU201900282 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 數學系 |
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ntu-108-1.pdf Restricted Access | 693.27 kB | Adobe PDF |
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