원분체 (cyclotomic field) - 편집 역사

2021년 2월 17일 (수) 12:55에 Pythagoras0님의 편집

2021-02-17T12:55:37Z

2020-12-28T14:29:19Z

메타데이터: 새 문단

2014-07-11T02:48:24Z

2014-07-11T02:44:47Z

2014-07-10T23:42:59Z

2014-07-10T05:29:19Z

2014-05-07T01:53:57Z

2014-05-07T01:35:12Z

2014-01-10T11:54:18Z

2014-01-10T11:53:14Z

@@ 91번째 줄: / 91번째 줄: @@
 * Lawrence C. Washington, Introduction to Cyclotomic Fields, Graduate Texts in Mathematics, 83. Springer-Verlag, New York, 1982
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q1554628 Q1554628]

← 이전 판		2020년 12월 28일 (월) 14:29 판
90번째 줄:		90번째 줄:

	* Lawrence C. Washington, Introduction to Cyclotomic Fields, Graduate Texts in Mathematics, 83. Springer-Verlag, New York, 1982		* Lawrence C. Washington, Introduction to Cyclotomic Fields, Graduate Texts in Mathematics, 83. Springer-Verlag, New York, 1982
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q1554628 Q1554628]

@@ 43번째 줄: / 43번째 줄: @@
 ==유수(class number)==
 ==메모==
 * Barry Mazur [http://www.ams.org/journals/bull/2011-48-02/S0273-0979-2011-01326-X/home.html How can we construct abelian Galois extensions of basic number fields?] Bull. Amer. Math. Soc. 48 (2011), 155-209.
@@ 67번째 줄: / 60번째 줄: @@
 ==관련된 항목들==
 * [[원분다항식(cyclotomic polynomial)]]
 * [[이차 수체(quadratic number fields) 의 정수론]]

@@ 12번째 줄: / 12번째 줄: @@
 * <math>\zeta_n</math>는 원시 n-단위근
 * <math>K = \mathbb Q(\zeta_n)</math>
@@ 93번째 줄: / 91번째 줄: @@
 * http://en.wikipedia.org/wiki/cyclotomic_field
 * http://www.encyclopediaofmath.org/index.php/Cyclotomic_field

@@ 57번째 줄: / 57번째 줄: @@
 * [http://staff.miyakyo-u.ac.jp/~taya/jk2008/abst/fukuda-komatsu.pdf Weber class number problem]
 * Barry Mazur [http://www.ams.org/journals/bull/2011-48-02/S0273-0979-2011-01326-X/home.html How can we construct abelian Galois extensions of basic number fields?] Bull. Amer. Math. Soc. 48 (2011), 155-209.
@@ 101번째 줄: / 100번째 줄: @@
 * Miller, John C. “Real Cyclotomic Fields of Prime Conductor and Their Class Numbers.” arXiv:1407.2373 [math], July 9, 2014. http://arxiv.org/abs/1407.2373.
 * Miller, John C. “Class Numbers of Totally Real Fields and Applications to the Weber Class Number Problem.” arXiv:1405.1094 [math], May 5, 2014. http://arxiv.org/abs/1405.1094.
 * Schoof, René. "Class numbers of real cyclotomic fields of prime conductor." Mathematics of computation 72.242 (2003): 913-937.
 * Hajir, Farshid, and Fernando Rodriguez Villegas. 1997. “Explicit Elliptic Units, I.” Duke Mathematical Journal 90 (3) (December): 495–521. doi:10.1215/S0012-7094-97-09013-X.

@@ 5번째 줄: / 5번째 줄: @@
 * class field theory
 * Iwasawa theory
@@ 101번째 줄: / 99번째 줄: @@
 ==관련논문==
 * Miller, John C. “Class Numbers of Totally Real Fields and Applications to the Weber Class Number Problem.” arXiv:1405.1094 [math], May 5, 2014. http://arxiv.org/abs/1405.1094.
 * Schoof, René. "Class numbers of real cyclotomic fields of prime conductor." Mathematics of computation 72.242 (2003): 913-937.

← 이전 판	2014년 1월 10일 (금) 11:54 판
82번째 줄:	82번째 줄:


−	+	==매스매티카 파일 및 계산 리소스==
	+	* https://docs.google.com/file/d/0B8XXo8Tve1cxME1PNGVkOEtsRmc/edit

@@ 41번째 줄: / 41번째 줄: @@
 * <math>K = \mathbb Q(\zeta_n)</math>에 대한 [[데데킨트 제타함수]]
 :<math>\zeta_{K}(s)=\sum_{\mathfrak{a} \text{:ideals}}\frac{1}{N(\mathfrak{a})^s}=\prod_{\mathfrak{p} \text{:prime ideals}} \frac{1}{1-N(\mathfrak{p})^{-s}}</math>
-*  제타함수의 분해:<math>\zeta_K(s)=\prod_{\chi\in \tilde{G}}L(s,\chi)</math> 로부터 [[등차수열의 소수분포에 관한 디리클레 정리]] 를 얻을 수 있다
+* 제타함수의 분해:<math>\zeta_K(s)=\prod_{\chi\in \tilde{G}}L(s,\chi)</math>
 * 자세한 내용은 [[원분체의 데데킨트 제타함수]] 항목 참조
-==class number==
+==유수(class number)==
-* <math>K = \mathbb Q(\zeta_n)</math> 의 class number <math>h_K</math>
+* <math>K = \mathbb Q(\zeta_n)</math> 의유수 <math>h_K</math>
 * <math>K^{+} :=\mathbb Q(\zeta_n)^{+}=K\cap \mathbb{R}</math>
 * <math>h_K=h_K^{+}h_K^{-}</math>
-* <math>h_K^{-}</math>를 relative class number라 한다
+* <math>h_K^{-}</math>를 상대적 유수(relative class number)라 한다
@@ 109번째 줄: / 109번째 줄: @@
 ==관련도서==
-*  Introduction to Cyclotomic Fields
+* Lawrence C. Washington, Introduction to Cyclotomic Fields, Graduate Texts in Mathematics, 83. Springer-Verlag, New York, 1982