데데킨트 제타함수 - 편집 역사

Pythagoras0: /* 메타데이터 */

2021-02-26T09:41:50Z

메타데이터

Pythagoras0: /* 메타데이터 */ 새 문단

2021-02-26T09:36:25Z

메타데이터: 새 문단

Pythagoras0: /* 노트 */ 새 문단

2021-02-26T09:36:21Z

노트: 새 문단

2021년 2월 17일 (수) 12:02에 Pythagoras0님의 편집

2021-02-17T12:02:45Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-28T14:34:49Z

메타데이터: 새 문단

2020년 11월 16일 (월) 11:59에 Pythagoras0님의 편집

2020-11-16T11:59:19Z

Pythagoras0: /* 관련논문 */

2014-10-20T08:58:48Z

Pythagoras0: /* Klingen-Siegel 정리 */

2014-10-20T08:53:09Z

Klingen-Siegel 정리

2014년 7월 13일 (일) 05:00에 Pythagoras0님의 편집

2014-07-13T05:00:50Z

2014년 1월 2일 (목) 00:19에 Pythagoras0님의 편집

2014-01-02T00:19:55Z

← 이전 판		2021년 2월 26일 (금) 09:41 판
119번째 줄:		119번째 줄:

	[[분류:정수론]]		[[분류:정수론]]
−
−	~~==메타데이터==~~
−	~~===위키데이터===~~
−	* ID : [https://www.wikidata.org/wiki/Q1182160 Q1182160]
−	~~===Spacy 패턴 목록===~~
−	* [{'LOWER': 'dedekind'}, {'LOWER': 'zeta'}, {'LEMMA': 'function'}]
−	* [{'LOWER': 'dedekind'}, {'LOWER': "'s"}, {'LOWER': 'zeta'}, {'LEMMA': 'function'}]

	== 노트 ==		== 노트 ==

← 이전 판		2021년 2월 26일 (금) 09:36 판
146번째 줄:		146번째 줄:
	===소스===		===소스===
	<references />		<references />
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q1182160 Q1182160]
		+	===Spacy 패턴 목록===
		+	* [{'LOWER': 'dedekind'}, {'LOWER': 'zeta'}, {'LOWER': 'function'}]
		+	* [{'LOWER': 'dedekind'}, {'LOWER': "'s"}, {'LOWER': 'zeta'}, {'LOWER': 'function'}]

← 이전 판		2021년 2월 26일 (금) 09:36 판
126번째 줄:		126번째 줄:
	* [{'LOWER': 'dedekind'}, {'LOWER': 'zeta'}, {'LEMMA': 'function'}]		* [{'LOWER': 'dedekind'}, {'LOWER': 'zeta'}, {'LEMMA': 'function'}]
	* [{'LOWER': 'dedekind'}, {'LOWER': "'s"}, {'LOWER': 'zeta'}, {'LEMMA': 'function'}]		* [{'LOWER': 'dedekind'}, {'LOWER': "'s"}, {'LOWER': 'zeta'}, {'LEMMA': 'function'}]
		+
		+	== 노트 ==
		+
		+	===말뭉치===
		+	# In particular some of these pairs have different class numbers, so the Dedekind zeta function of a number field does not determine its class number.<ref name="ref_ca3cd66b">[https://en.wikipedia.org/wiki/Dedekind_zeta_function Dedekind zeta function]</ref>
		+	# For K K a number field then all special values of the Dedekind zeta function ζ K ( n ) \zeta_K(n) for integer n n happen to be periods (MO comment).<ref name="ref_8e168495">[https://ncatlab.org/nlab/show/Dedekind+zeta+function Dedekind zeta function in nLab]</ref>
		+	# Just like the Riemann zeta function, each Dedekind zeta function possesses a functional equation.<ref name="ref_96a08161">[https://www.theochem.ru.nl/~pwormer/Knowino/knowino.org/wiki/Dedekind_zeta_function.html Dedekind zeta function]</ref>
		+	# The nontrivial zeros of the Dedekind zeta function of any algebraic number eld lie on the critical line: Re(s) = 1/2.<ref name="ref_e51d5cc2">[http://archive.schools.cimpa.info/archivesecoles/20171023105958/PV-lecture2.pdf Introduction to l-functions:]</ref>
		+	# Theorem Let X be a group of Dirichlet characters, K the associated eld, and K (s) the Dedekind zeta function of K .<ref name="ref_e51d5cc2" />
		+	# From there, we discuss algebraic number elds and introduce the tools needed to dene the Dedekind zeta function.<ref name="ref_d04421dc">[https://math.uchicago.edu/~may/REU2016/REUPapers/Baidoo.pdf Dirichlet l-functions and dedekind ζ-functions]</ref>
		+	# 1 2 FRIMPONG A. BAIDOO necessary for providing context to the Dedekind zeta function.<ref name="ref_d04421dc" />
		+	# In section 9, we then dene the Dedekind zeta function, describe the ideal class group and then highlight the Dedekind zeta functions role in the class number formula.<ref name="ref_d04421dc" />
		+	# I was trying to learn a little about the Dedekind zeta function.<ref name="ref_c73b2fb0">[https://math.stackexchange.com/questions/33006/relation-between-the-dedekind-zeta-function-and-quadratic-reciprocity Relation between the Dedekind Zeta Function and Quadratic Reciprocity]</ref>
		+	# For a cubic extension K 3 /ℚ, which is not normal, new results on the behavior of mean values of the Dedekind zeta function of the field K 3 in the critical strip are obtained.<ref name="ref_2c7bf667">[https://link.springer.com/article/10.1007/s10958-008-0126-9 Mean values connected with the Dedekind zeta function]</ref>
		+	# We study analytic aspects of the Dedekind zeta function of a Galois extension.<ref name="ref_2aacc359">[https://core.ac.uk/download/pdf/18451908.pdf Moments of the dedekind zeta function]</ref>
		+	# In the rst part of this thesis we give a formula for the second moment of the Dedekind zeta function of a quadratic eld times an arbitrary Dirichlet polynomial of length T 1/11(cid:15).<ref name="ref_2aacc359" />
		+	# In the second part, we derive a hybrid Euler-Hadamard product for the Dedekind zeta function of an arbitrary number eld.<ref name="ref_2aacc359" />
		+	# We then conjecture that the 2kth moment of the Dedekind zeta function of a Galois extension is given by the product of the two.<ref name="ref_2aacc359" />
		+	===소스===
		+	<references />

@@ 120번째 줄: / 120번째 줄: @@
 [[분류:정수론]]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q1182160 Q1182160]

← 이전 판		2020년 12월 28일 (월) 14:34 판
119번째 줄:		119번째 줄:

	[[분류:정수론]]		[[분류:정수론]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q1182160 Q1182160]

@@ 53번째 줄: / 53번째 줄: @@
 * F : totally real 수체
 * <math>[F: \mathbb{Q}]=n</math>
-* $m>0$일 때, 다음을 만족하는 적당한 유리수 <math>r(m)\in \mathbb{Q}</math>가 존재한다
+* <math>m>0</math>일 때, 다음을 만족하는 적당한 유리수 <math>r(m)\in \mathbb{Q}</math>가 존재한다
 :<math>\zeta_{F}(2m)=r(m)\frac{\pi^{2mn}}{\sqrt{|d_{F}|}}</math>
 * http://planetmath.org/SiegelKlingenTheorem.html
@@ 59번째 줄: / 59번째 줄: @@
 ===Zagier, Bloch, Suslin===
 * <math>[K : \mathbb{Q}] = r_1 + 2r_2</math>일 때,
-:<math>\zeta_{K}(2)\sim_{\mathbb{Q^{\times}}} \frac{\pi^{2(r_1 + r_2)}}{\sqrt{|d_{K}|}}\det\{D(\sigma_i(\xi_j))\}_{1\leq i,j\leq r_2}</math> 여기서 <math>\xi_i,(i=1,\cdots, r_2)</math> 는 Bloch group <math>B(K)\otimes \mathbb{Q}</math>의 $\mathbb{Q}$-basis D는 [[블로흐-비그너 다이로그(Bloch-Wigner dilogarithm)]] 함수이며, <math>a\sim_{\mathbb{Q^{\times}}} b</math> 는 <math>a/b\in\mathbb{Q}</math> 를 의미함
+:<math>\zeta_{K}(2)\sim_{\mathbb{Q^{\times}}} \frac{\pi^{2(r_1 + r_2)}}{\sqrt{|d_{K}|}}\det\{D(\sigma_i(\xi_j))\}_{1\leq i,j\leq r_2}</math> 여기서 <math>\xi_i,(i=1,\cdots, r_2)</math> 는 Bloch group <math>B(K)\otimes \mathbb{Q}</math>의 <math>\mathbb{Q}</math>-basis D는 [[블로흐-비그너 다이로그(Bloch-Wigner dilogarithm)]] 함수이며, <math>a\sim_{\mathbb{Q^{\times}}} b</math> 는 <math>a/b\in\mathbb{Q}</math> 를 의미함

@@ 110번째 줄: / 110번째 줄: @@
 ==관련논문==
+* Zagier, Don. ‘Hyperbolic Manifolds and Special Values of Dedekind Zeta-Functions’. Inventiones Mathematicae 83, no. 2 (1 June 1986): 285–301. doi:[http://www.springerlink.com/content/v36272439g3g5006/ 10.1007/BF01388964].
 * D. Zagier, [http://people.mpim-bonn.mpg.de/zagier/files/scanned/PolylogsDedekindZetaAndKTheory/fulltext.pdf Polylogarithms, Dedekind zeta functions and the algebraic K-theory of fields]
-*  Commensurability classes and volumes of hyperbolic 3-manifolds
+* Borel, A. ‘Commensurability Classes and Volumes of Hyperbolic 3-Manifolds’. Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze 8, no. 1 (1981): 1–33.

@@ 90번째 줄: / 90번째 줄: @@
 ==계산 리소스==
 * https://docs.google.com/file/d/0B8XXo8Tve1cxcXFHOEFSMHc1bUk/edit
+* [http://www.math.mcgill.ca/goren/ZetaValues/zeta.html Tables of Values of Dedekind Zeta Functions]
 ==사전 형태의 자료==
@@ 101번째 줄: / 100번째 줄: @@
-==리뷰논문, 에세이, 강의노트==
+==리뷰, 에세이, 강의노트==
 *  H. M. Stark, "Galois theory, algebraic number theory and zeta functions" ,in \ From number theory to physics", ed. M. Walschmidt, P. Moussa, J.-M. Luck, C. Itzykson Springer
 *  H. M. Stark, The analytic theory of algebraic numbers http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bams/1183537391
@@ 115번째 줄: / 113번째 줄: @@
 * [http://www.springerlink.com/content/v36272439g3g5006/ Hyperbolic manifolds and special values of Dedekind zeta-functions]
 ** Don Zagier, Inventiones Mathematicae, Volume 83, Number 2 / 1986년 6월
-* D. Zagier, Polylogarithms, Dedekind zeta functions and the algebraic K-theory of fields http://people.mpim-bonn.mpg.de/zagier/files/scanned/PolylogsDedekindZetaAndKTheory/fulltext.pdf
+* D. Zagier, [http://people.mpim-bonn.mpg.de/zagier/files/scanned/PolylogsDedekindZetaAndKTheory/fulltext.pdf Polylogarithms, Dedekind zeta functions and the algebraic K-theory of fields]
 *  Commensurability classes and volumes of hyperbolic 3-manifolds
 ** A. Borel, Ann. Sc. Norm. Super. Pisa8, 1–33 (1981)
 [[분류:정수론]]

@@ 85번째 줄: / 85번째 줄: @@
 * [[디리클레 유수 (class number) 공식]]
 * [[이차 수체에 대한 디리클레 class number 공식 |이차 수체에 대한 디리클레 class number 공식]]
-* [[L-함수의 값 구하기 입문]]