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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳其誠(Ki-Seng Tan) | |
| dc.contributor.author | Wei-Lun Tsai | en |
| dc.contributor.author | 蔡維倫 | zh_TW |
| dc.date.accessioned | 2021-06-16T23:44:54Z | - |
| dc.date.available | 2012-08-01 | |
| dc.date.copyright | 2012-08-01 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2012-07-24 | |
| dc.identifier.citation | [1] Gerald J. Janusz. Algebraic number elds. Providence, R.I. American Mathematical Society, c1996.
[2] Joseph H. Silverman.The Arithmetic of Elliptic Curves. Springer-Verlag, GTM 106, 1986. [3] J.W.S. Cassels and A. Frohlich (eds.)Algebraic Number Theory. London, Academic Press Inc 1986. [4] J.S. Milne.Arithmetic Duality Theorems .ISBN 141964274X:,c2006. [5] J.S. Milne.Elliptic Curves. ISBN-10: 1419652575, 2006. [6] Ken Ono.Twists Of Elliptic Curves.Compositio Mathematica 106, 1997, pp. 349-360. [7] Lawrence C.Washington. Elliptic Curves: Number Theory and Cryptography.CRC Press, Boca Raton,c2008. [8] N. Koblitz. Introduction To Elliptic Curves And Modular Forms. Springer-Verlag 1984. [9] Paul Monsky.Mock heegner points and congruent numbers. Mathematische Zeitschrift, 1990, Volume 204. [10] Wen-Chen Chi,Hung-Min Liao,Ki-Seng Tan. On The Rank Of Quadratic Twist Of An Elliptic Curve. [11] Wen-Chen Chi,King-Fai Lai,Ki-Seng Tan. Integer Points On Elliptic Curves. P.J.M,Vol. 222, No. 2, 2005. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/65468 | - |
| dc.description.abstract | 首先我們給出同餘數的定義以及其性質。然後介紹肯-小野猜想。最後應用論文[10]中的方法和推廣來處理同餘數的問題。 | zh_TW |
| dc.description.abstract | We review the theory of congruent numbers and Ken Ono's Conjecture. We also study the technique developed in [10] and then apply it to the congruent number problem. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T23:44:54Z (GMT). No. of bitstreams: 1 ntu-101-R99221014-1.pdf: 1917586 bytes, checksum: 697a14209ed788fdf9b0b3c2bdbb7a9d (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | Acknowlegement ......i
中文摘要......ii Abstract ......iii Contents ......iv List of Tables ......v 1. Introduction. ......1 2. The congruent number problem ......7 2.1. Twists of the congruent elliptic curve ......7 2.2. Tunnell's Theorem ......9 2.3. Exampls ......10 3. Selmer groups over quadratic extensions ......13 3.1. The Kummer exact sequence ......13 3.2. Selmer groups ......14 3.3. The strategy of computing the 2-Selmer group ......17 3.4. The 2-Selmer group of the congruent curve over Q ....19 3.5. Proof of Lemma 1.0.1 and Lemma 1.0.2 ......23 4. Quadratic twists of the congruent curve ......25 4.1. The computation on local points ......25 4.2. The proofs of Theorem 1.3 and Theorem 1.4...... 27 References ......29 | |
| dc.language.iso | en | |
| dc.subject | 同餘數 | zh_TW |
| dc.subject | 秩 | zh_TW |
| dc.subject | 二次扭變 | zh_TW |
| dc.subject | congruent number | en |
| dc.subject | quadratic twist | en |
| dc.subject | rank | en |
| dc.title | 計算橢圓曲線二次扭變的秩與肯·小野猜想 | zh_TW |
| dc.title | The Rank of Twists of Elliptic Curves and Ken Ono's Conjecture | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 紀文鎮(Wen-Chen Chi),黃柏嶧(Po-Yi Huang) | |
| dc.subject.keyword | 秩,二次扭變,同餘數, | zh_TW |
| dc.subject.keyword | rank,quadratic twist,congruent number, | en |
| dc.relation.page | 30 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2012-07-24 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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