자코비 세타함수

간단한 소개

• 세타함수의 정의 (spectral decomposition of heat kernel)
  \(\theta(\tau)= \sum_{n=-\infty}^\infty \exp(\pi i n^2\tau)\)
  

 

세타함수의 Modularity

\(\theta(-\frac{1}{\tau})=\sqrt{\frac{\tau}{i}} \theta({\tau})\)

\(\tau=iy, y>0\) 으로 쓰면,

\(\theta(\frac{i}{y})=\sqrt{y} \theta({iy)\)

 

 

 

 

 

 

관련된 다른 주제들

• 타원함수
• 이차형식

 

표준적인 도서 및 추천도서

• Brief Introduction to Theta Functions
  
  • BELLMAN, RICHARD
• Tata Lectures on Theta I,II,III
  
  • David Mumford

위키링크

• http://en.wikipedia.org/wiki/Theta_functions

 

참고할만한 자료

• Applications of Theta Functions to Arithmetic
  
  • G. D. Nichols
  • The American Mathematical Monthly, Vol. 45, No. 6 (Jun. - Jul., 1938), pp. 363-368
• A First Course in Modular Forms (Graduate Texts in Mathematics)
  
  • Fred Diamond and Jerry Shurman
  • 18-19p four_square_theorem_and_theta_funtion.pdf
• Karl Gustav Jacob Jacobi
  
  • Jacobi's Four Square Theorem. (Also available in postscript format [11 pages].) [CONSTRUCTION IN PROGRESS]