버치와 스위너톤-다이어 추측 - 편집 역사

2021년 2월 17일 (수) 11:47에 Pythagoras0님의 편집

2021-02-17T11:47:05Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-28T14:50:14Z

메타데이터: 새 문단

2020년 11월 13일 (금) 05:10에 Pythagoras0님의 편집

2020-11-13T05:10:57Z

Pythagoras0: /* 관련논문 */

2015-12-25T10:19:59Z

Pythagoras0: /* 관련논문 */

2015-09-03T13:07:38Z

Pythagoras0: /* 관련논문 */

2014-11-18T04:43:04Z

2014년 6월 24일 (화) 15:40에 Pythagoras0님의 편집

2014-06-24T15:40:14Z

2014년 4월 4일 (금) 02:30에 Pythagoras0님의 편집

2014-04-04T02:30:45Z

Pythagoras0: Pythagoras0 사용자가 Birch and Swinnerton-Dyer 추측 문서를 버치와 스위너톤-다이어 추측 문서로 옮겼습니다.

2014-01-03T23:44:43Z

Pythagoras0 사용자가 Birch and Swinnerton-Dyer 추측 문서를 버치와 스위너톤-다이어 추측 문서로 옮겼습니다.

2014년 1월 3일 (금) 23:44에 Pythagoras0님의 편집

2014-01-03T23:44:24Z

@@ 101번째 줄: / 101번째 줄: @@
 ** Joe P. Buhler, Benedict H. Gross and Don B. Zagier, Mathematics of Computation, Vol. 44, No. 170 (Apr., 1985), pp. 473-481
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q671993 Q671993]

← 이전 판		2020년 12월 28일 (월) 14:50 판
100번째 줄:		100번째 줄:
	* [http://www.jstor.org/stable/2007967 On the Conjecture of Birch and Swinnerton-Dyer for an Elliptic Curve of Rank 3]		* [http://www.jstor.org/stable/2007967 On the Conjecture of Birch and Swinnerton-Dyer for an Elliptic Curve of Rank 3]
	** Joe P. Buhler, Benedict H. Gross and Don B. Zagier, Mathematics of Computation, Vol. 44, No. 170 (Apr., 1985), pp. 473-481		** Joe P. Buhler, Benedict H. Gross and Don B. Zagier, Mathematics of Computation, Vol. 44, No. 170 (Apr., 1985), pp. 473-481
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q671993 Q671993]

@@ 89번째 줄: / 89번째 줄: @@
 ==관련논문==
-* Bruin, Peter, and Andrea Ferraguti. “On $L$-Functions of Quadratic $\mathbb{Q}$-Curves.” arXiv:1511.09001 [math], November 29, 2015. http://arxiv.org/abs/1511.09001.
+* Bruin, Peter, and Andrea Ferraguti. “On <math>L</math>-Functions of Quadratic <math>\mathbb{Q}</math>-Curves.” arXiv:1511.09001 [math], November 29, 2015. http://arxiv.org/abs/1511.09001.
 * Ota, Kazuto. “Kato’s Euler System and the Mazur-Tate Refined Conjecture of BSD Type.” arXiv:1509.00682 [math], September 2, 2015. http://arxiv.org/abs/1509.00682.
 * Balakrishnan, Jennifer, Ishai Dan-Cohen, Minhyong Kim, and Stefan Wewers. ‘A Non-Abelian Conjecture of Birch and Swinnerton-Dyer Type for Hyperbolic Curves’. arXiv:1209.0640 [math], 4 September 2012. http://arxiv.org/abs/1209.0640.

@@ 89번째 줄: / 89번째 줄: @@
 ==관련논문==
 * Ota, Kazuto. “Kato’s Euler System and the Mazur-Tate Refined Conjecture of BSD Type.” arXiv:1509.00682 [math], September 2, 2015. http://arxiv.org/abs/1509.00682.
 * Balakrishnan, Jennifer, Ishai Dan-Cohen, Minhyong Kim, and Stefan Wewers. ‘A Non-Abelian Conjecture of Birch and Swinnerton-Dyer Type for Hyperbolic Curves’. arXiv:1209.0640 [math], 4 September 2012. http://arxiv.org/abs/1209.0640.

@@ 89번째 줄: / 89번째 줄: @@
 ==관련논문==
 * Balakrishnan, Jennifer, Ishai Dan-Cohen, Minhyong Kim, and Stefan Wewers. ‘A Non-Abelian Conjecture of Birch and Swinnerton-Dyer Type for Hyperbolic Curves’. arXiv:1209.0640 [math], 4 September 2012. http://arxiv.org/abs/1209.0640.
 * [http://www.mathnet.ru/eng/im1191 Finiteness of E(Q) and Sha(E, Q) for a subclass of Weil curves]

← 이전 판		2014년 6월 24일 (화) 15:40 판
54번째 줄:		54번째 줄:


		+
		+	==메모==
		+	* [http://www.sms.cam.ac.uk/media/1131073 Interview of Sir Peter Swinnerton-Dyer]
		+
		+
	==관련된 항목들==		==관련된 항목들==

@@ 77번째 줄: / 77번째 줄: @@
 ==리뷰, 에세이, 강의노트==
+* http://mattbakerblog.wordpress.com/2014/03/10/the-bsd-conjecture-is-true-for-most-elliptic-curves/
 * Wiles, A. "[http://www.claymath.org/millennium/Birch_and_Swinnerton-Dyer_Conjecture/BSD.pdf The Birch and Swinnerton-Dyer Conjecture]

← 이전 판	2014년 1월 3일 (금) 23:44 판
(차이 없음)

@@ 1번째 줄: / 1번째 줄: @@
 ==개요==
 * 타원곡선의 rank는 잘 알려져 있지 않다
 * Birch and Swinnerton-Dyer 추측은 타원곡선의 rank에 대한 밀레니엄 추측의 하나이다
@@ 19번째 줄: / 18번째 줄: @@
 * Hasse-Weil 제타함수라고도 함
-*  타원 곡선 E의 conductor가 N일 때, 다음과 같이 정의됨:<math>L(s,E)=\prod_p L_p (s,E)^{-1}</math><br> 여기서 :<math>L_p(s,E)=\left\{\begin{array}{ll}(1-a_pp^{-s}+p^{1-2s}), & \mbox{if }p \nmid N \\ (1-a_pp^{-s}), & \mbox{if }p||N \\             1, & \mbox{if }p^2|N \end{array}\right.</math><br>
+*  타원 곡선 E의 conductor가 N일 때, 다음과 같이 정의됨:<math>L(s,E)=\prod_p L_p (s,E)^{-1}</math> 여기서 :<math>L_p(s,E)=\left\{\begin{array}{ll}(1-a_pp^{-s}+p^{1-2s}), & \mbox{if }p \nmid N \\ (1-a_pp^{-s}), & \mbox{if }p||N \\             1, & \mbox{if }p^2|N \end{array}\right.</math>
 * 여기서 <math>a_p</math>는 유한체위에서의 해의 개수와 관련된 정수
@@ 28번째 줄: / 27번째 줄: @@
 ==추측==
-* <math>E(\mathbb{Q})=\mathbb{Z}^r \oplus E(\mathbb{Q})_{\operatorname{Tor}}</math>의 rank r은 <math>\operatorname{Ord}_{s=1}L(s,E)</math>와 같다<br>
+* <math>E(\mathbb{Q})=\mathbb{Z}^r \oplus E(\mathbb{Q})_{\operatorname{Tor}}</math>의 rank r은 <math>\operatorname{Ord}_{s=1}L(s,E)</math>와 같다
@@ 44번째 줄: / 43번째 줄: @@
 ==역사==
-* The Birch and Swinnerton-Dyer conjecture has been proved only in special cases :<br>
+* The Birch and Swinnerton-Dyer conjecture has been proved only in special cases :
 # In 1976 [http://en.wikipedia.org/wiki/John_Coates_%28mathematician%29 John Coates] and [http://en.wikipedia.org/wiki/Andrew_Wiles Andrew Wiles] proved that if <em>E</em> is a curve over a number field <em>F</em> with complex multiplication by an imaginary quadratic field <em>K</em> of [http://en.wikipedia.org/wiki/Class_number_ %28 number_theory %29 class number] 1, <em>F=K</em> or '''Q''', and <em>L(E,1)</em> is not 0 then <em>E</em> has only a finite number of rational points. This was extended to the case where <em>F</em> is any finite abelian extension of <em>K</em> by Nicole Arthaud-Kuhman, who shared an office with Wiles when both were students of Coates at Stanford.
@@ 51번째 줄: / 50번째 줄: @@
 # In 1991 [http://en.wikipedia.org/wiki/Karl_Rubin Karl Rubin] showed that for elliptic curves defined over an imaginary quadratic field <em>K</em> with complex multiplication by <em>K</em>, if the <em>L</em>-series of the elliptic curve was not zero at <em>s=1</em>, then the <em>p</em>-part of the Tate-Shafarevich group had the order predicted by the Birch and Swinnerton-Dyer conjecture, for all primes <em>p > 7</em>.
 # In 1999 [http://en.wikipedia.org/wiki/Andrew_Wiles Andrew Wiles], [http://en.wikipedia.org/wiki/Christophe_Breuil Christophe Breuil], [http://en.wikipedia.org/wiki/Brian_Conrad Brian Conrad], [http://en.wikipedia.org/wiki/Fred_Diamond Fred Diamond] and [http://en.wikipedia.org/wiki/Richard_Taylor_ %28 mathematician %29 Richard Taylor] proved that all elliptic curves defined over the rational numbers are modular (the [http://en.wikipedia.org/wiki/Taniyama-Shimura_theorem Taniyama-Shimura theorem]), which extends results 2 and 3 to all elliptic curves over the rationals.
 *  Nothing has been proved for curves with rank greater than 1, although there is extensive numerical evidence for the truth of the conjecture.
 * [[수학사 연표]]
-−
 ==관련된 항목들==
@@ 76번째 줄: / 63번째 줄: @@
 ==수학용어번역==
+* {{forvo|url=Birch}}
-* 단어사전 http://www.google.com/dictionary?langpair=en|ko&q=
+* {{forvo|url=Swinnerton-Dyer}}
@@ 91번째 줄: / 72번째 줄: @@
 * http://ko.wikipedia.org/wiki/
 * http://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture
-==expository==
+==리뷰, 에세이, 강의노트==
 * Wiles, A. "[http://www.claymath.org/millennium/Birch_and_Swinnerton-Dyer_Conjecture/BSD.pdf The Birch and Swinnerton-Dyer Conjecture]
@@ 111번째 줄: / 85번째 줄: @@
 ==관련논문==
-* [http://www.mathnet.ru/eng/im1191 Finiteness of E(Q) and Sha(E, Q) for a subclass of Weil curves]<br>
+* [http://www.mathnet.ru/eng/im1191 Finiteness of E(Q) and Sha(E, Q) for a subclass of Weil curves]
 ** V. Kolyvagin, (transl.) Math. USSR-Izv. 32 (1989), no. 3, 523--541
 * [http://dx.doi.org/10.1007%2FBF01458081 Heegner points and derivatives of L-series. II]
-* [http://dx.doi.org/10.1007%2FBF01458081 Heegner points and derivatives of L-series. II]<br>
+**  Gross, B.; Kohnen, W.; Zagier, D. (1987),  Mathematische Annalen 278 (1\[Dash]4): 497-562
-**  Gross, B.; Kohnen, W.; Zagier, D. (1987),  Mathematische Annalen 278 (1\[Dash]4): 497\[Dash]562<br>
+* [http://dx.doi.org/10.1007%2FBF01388809 Heegner points and derivatives of L-series]
-* [http://dx.doi.org/10.1007%2FBF01388809 Heegner points and derivatives of L-series]<br>
+**  Gross, Benedict H.; Zagier, Don B. (1986),  Inventiones Mathematicae 84 (2): 225-320
-**  Gross, Benedict H.; Zagier, Don B. (1986),  Inventiones Mathematicae 84 (2): 225\[Dash]320<br>
+* [http://www.jstor.org/stable/2007967 On the Conjecture of Birch and Swinnerton-Dyer for an Elliptic Curve of Rank 3]
 ** Joe P. Buhler, Benedict H. Gross and Don B. Zagier, Mathematics of Computation, Vol. 44, No. 170 (Apr., 1985), pp. 473-481