研究生: |
李忠穎 |
---|---|
論文名稱: |
Computations on the Deuring Correspondence of Supersingular Elliptic Curves Computations on the Deuring Correspondence of Supersingular Elliptic Curves |
指導教授: | 紀文鎮 |
學位類別: |
碩士 Master |
系所名稱: |
數學系 Department of Mathematics |
論文出版年: | 2007 |
畢業學年度: | 95 |
語文別: | 英文 |
論文頁數: | 25 |
中文關鍵詞: | 橢圓曲線 |
英文關鍵詞: | elliptic curve, supersingular, Deuring, Pizer |
論文種類: | 學術論文 |
相關次數: | 點閱:156 下載:1 |
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此篇論文是以實際例子 p=41 之情形, 驗證 Deuring Theorem 的對應性.
[D1] M. Deuring, Die Anzahl der von Maximalordnungen einer
definiten Quaternionenalgebra mit primer Grundzahl, Jber.
Deutch. Math. Verein. 54(1950),24-41.
[D2] M. Deuring, Die Typen der Multiplikatorenringe elliptischer Funktionenkorper, Abh. Math. Sem. Hamburg 14(1941), 197-272.
[M-L] K. MacMurdy and K. Lauter, Explicit Generators for Endomorphism Rings of Supersingular Elliptic Cruves, Preprint, August 2, 2004
[P1] A. Pizer, The action of the canonical involution ~on
modular forms of weight 2 on \Gamma _0 (M), Math. Ann. 226(1977),99-116.
[P2] A. Pizer, A note on a conjecture of Hecke, Pacific J.
Math. 79(1978), no.2, 541-548.
[P3] A. Pizer, An algorithm for computing modular forms on \Gamma_0 (N), J. Algebra 64(1980), no.2, 340-390.
[Sil] J. Silverman, The Arithmetic of Elliptic Curves,
Graduate Texts in Mathematics 106, Springer-Verlag New York, 1986.