簡易檢索 / 詳目顯示

回結果列表
研究生： 林子閔
Lin, Zi-Min
論文名稱： 函數體上橢圓曲線之有理扭點的計算
Computation on Rational Torsions of Elliptic Curves over Function Fields
指導教授： 魏福村
Wei, Fu-Tsun
口試委員: 張介玉
Chang, Chieh-Yu
洪斌哲
Hung, Pin-Chi
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： 2022
畢業學年度： 110
語文別： 英文
論文頁數： 29
中文關鍵詞： 數論 、代數幾何 、橢圓曲線 、函數體 、複分析
外文關鍵詞： Number theory, Algebraic geometry, Elliptic curve, Function field, Complex analysis
相關次數： 點閱：1  下載：0 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 在本篇論文中，首先討論了函數體上橢圓曲線有理扭點的整數性。之後加入了類似於Mazur-Ogg的上界，我們整合出計算在函數體上橢圓曲線有理扭點的演算法。

    In this thesis, we first discuss about the integrality of the rational torsion points of elliptic curves over function fields. Together with an analogue of the Mazur-Ogg's bound, we derive an algorithm to compute the rational torsion points of elliptic curves over function fields.

    Content Computation on Rational Torsions of Elliptic Curves over Function Fields...............................5 Introduction.......................................5 Preliminary........................................7 Integral Property about the Non-p-torsion points...8 Division Polynomial................................12 Bound of the order of the torsion points...........15 Algorithm..........................................19 Appendix...........................................21 A. Proof of Theorem 4.4............................21 B. Computational data..............................26 Appendix. Bibliography.............................29

    [1]B.Mazur.Modular curves and the Eisenstein idealInst. Hautes Etudes Sci. Publ. Math. 47, 33–186(1978/1977)
    [2] B. Mazur.Rational isogenies of prime degree (with an appendix by D. Goldfeld)Invent. Math. 44(2),129–162 (1978)
    [3] Kenneth, H. Rosen, Ph.D.Elliptic Curve Number Theory and Cryptography Second Edition, 2008.
    [4] Joseph H. Silverman John T. TateRational Points on Elliptic Curves Second Edition
    [5] Joseph H. SilvermanThe Arithmetic of Elliptic Curves Second Edition
    [6] David A. Cox, Walter R. ParryTorsion in Elliptic Curve overk(t), Compositio Mathematica Vol. 41Fasc. 3 (1980) 337-354
    [7] Andreas Schweizer.On thepe-Torsion of Elliptic Curves and Elliptic Surfaces in Characteristicp,Transactions of the American Mathematical Society. Vol. 357 No. 3 1047–1059
    [8] J. F. VolochExplicitp-Descent for Elliptic Curves in Characteristicp, Compositio Mathematica tome74 No. 3 (1990) 247-258[9] [9] H. HasseBeweis des Analogons der Riemannschen Vermutung für die, Artinschen und F.K.Schmidtschen Kongruenzzetafunktionen in gewissen elliptischen Fallen. Nachr. Ges. Wiss. Göttingen,Math.-Phys. K. 253–262 (1933)
    [10] A. WeilSur les courbes algébriques et les variétés qui s’en déduisent.Actualités Sci. Ind., no. 1041 =Publ. Inst. Math. Univ. Strasbourg 7(1945). Hermann et Cie., Paris, 1948
    [11] https://math.mit.edu/classes/18.783/2015/LectureNotes5
    [12] https://math.mit.edu/classes/18.783/2015/LectureNotes6

    QR CODE