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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8738Full metadata record
| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 陳其誠 | |
| dc.contributor.author | Ban-Yan Su | en |
| dc.contributor.author | 蘇邦彥 | zh_TW |
| dc.date.accessioned | 2021-05-20T20:00:27Z | - |
| dc.date.available | 2010-02-24 | |
| dc.date.available | 2021-05-20T20:00:27Z | - |
| dc.date.copyright | 2010-02-24 | |
| dc.date.issued | 2010 | |
| dc.date.submitted | 2010-02-05 | |
| dc.identifier.citation | Joseph H. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986.
B. Mazur, Modular curves and the Eisenstein ideal, Publications Mathématiques de L'IHÉS Volume 47, Number 1 (1977), 33-186. Lawrence C. Washington, Introduction to Cyclotomic Fields, Springer, 1982. Daniel A. Marcus, Number Fields, Springer, 1977. Fred Diamond and John Im, Modular forms and modular curves, Seminar on Fermat's last theorem : 1993-1994, the Fields Institute for Research in the Mathematical Sciences, Toronto, Ontario, Canada (1995), 39-133. Yifan Yang, Defining equations of modular curves, Advances in Mathematics Volume 204, Issue 2 (2006), 481-508. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8738 | - |
| dc.description.abstract | 本論文考慮的問題是:考慮一個橢圓曲線上的有理點,若此有理點的階數是質數,則此質數可能是哪些?最後的結論是2,3,5,7,13.
第一章我們簡單介紹這個問題的來源,而在第二章和第三章我們回顧一些在證明中所需要用到的橢圓曲線性質以及Class Group的理論,並且在第四章證明這件事情. | zh_TW |
| dc.description.provenance | Made available in DSpace on 2021-05-20T20:00:27Z (GMT). No. of bitstreams: 1 ntu-99-R96221027-1.pdf: 252539 bytes, checksum: 3380a26d9ea3a3badf6a070176deead6 (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | Chapter 1. Introduction 2
Chapter 2. Properties of Elliptic Curves 4 2.1 The Weil pairing 4 2.2 Elliptic curves over local fields 6 2.3 Isogenies 8 Chapter 3. The Class Group 10 3.1 Ideal Class Group and Hilbert Class Field 10 3.2 Irregular Prime and Herbrand-Ribet Theorem 12 Chapter 4. The Proof of Theorem I 13 4.1 Faltings' theorem 13 4.2 The modular curves X0(p) and X1(p) 13 4.3 The field generated by E[p] 14 4.4 The proof 16 Bibliography 19 | |
| dc.language.iso | en | |
| dc.title | 橢圓曲線上有理點的質階數 | zh_TW |
| dc.title | The Prime Order of Rational Points on Elliptic Curves | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 98-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 紀文鎮,黎景輝,謝銘倫 | |
| dc.subject.keyword | 橢圓曲線,有理點, | zh_TW |
| dc.subject.keyword | Elliptic Curves,Rational Points, | en |
| dc.relation.page | 19 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2010-02-05 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| Appears in Collections: | 數學系 | |
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| File | Size | Format | |
|---|---|---|---|
| ntu-99-1.pdf | 246.62 kB | Adobe PDF | View/Open |
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