이차 수체에 대한 디리클레 유수 (class number) 공식

데데킨트 제타함수

\(\zeta_{K}(s)=\sum_{I \text{:ideals}}\frac{1}{N(I)^s}=\prod_{p \text{:prime ideals}} \frac{1}{1-N(p)^{-s}} \)

 

 

(정리) class number 공식

   \( \lim_{s\to 1} (s-1)\zeta_K(s)=\frac{2\pi h_K}{w_K \cdot \sqrt{|D_K|}}\)

 

 

 

 

 

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(정리) class number 공식

   \( \lim_{s\to 1} (s-1)\zeta_K(s)=\frac{2^{r_1}\cdot(2\pi)^{r_2}\cdot h_K\cdot \operatorname{Reg}_K}{w_K \cdot \sqrt{|D_K|}}\)

 

 

 

 

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관련된 다른 주제들

• 이차 수체(quadratic number fields) 의 정수론
  
  • Binary integral quadratic forms and Gauss' class number one problem
• The modular group, j-invariant and the singular moduli
• 타원적분, 타원함수, 타원곡선

 

관련도서 및 추천도서

• Primes of the Form x2 + ny2 : Fermat, Class Field Theory, and Complex Multiplication 
  
  • David A. Cox
• 도서내검색
  
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참고할만한 자료

• Lectures on the Dirichlet Class Number Formula for Imaginary Quadratic Fields
  
  • Tom Weston (personal webpage)
  • good introduction to the Dirichel class number formula for quadratic imaginary fields
• Gauss' class number problem for imaginary quadratic fields
  
  • Dorian Goldfeld.
  • Bull. Amer. Math. Soc. (N.S.) Volume 13, Number 1 (1985), 23-37
• A "Popular" Class Number Formula
  
  • Kurt Girstmair
  • The American Mathematical Monthly, Vol. 101, No. 10 (Dec., 1994), pp. 997-1001
• The Class Number Problem
  
  • Roy W. Ryden
  • The American Mathematical Monthly, Vol. 86, No. 3 (Mar., 1979), pp. 200-202
• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/Class_number_formula
• http://viswiki.com/en/
• http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
• http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
• 다음백과사전 http://enc.daum.net/dic100/search.do?q=
• 대한수학회 수학 학술 용어집

 

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