"Maass forms"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
9번째 줄: 9번째 줄:
 
<h5>Eisenstein series</h5>
 
<h5>Eisenstein series</h5>
  
−
<math>E(z,s) ={1\over 2}\sum_{(m,n)=1}{y^s\over|mz+n|^{2s}}</math>
+
* z = x + iy in the upper half-plane
 +
* Re(s) > 1
 +
* definition
 +
* <math>E(z,s) ={1\over 2}\sum_{(m,n)=1}{y^s\over|mz+n|^{2s}}</math>
  
 
<math>\DeltaE(z,s)=-y^2\left(\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}\right)E(z,s) = s(1-s)E(z,s)</math>
 
<math>\DeltaE(z,s)=-y^2\left(\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}\right)E(z,s) = s(1-s)E(z,s)</math>
17번째 줄: 20번째 줄:
 
 
 
 
  
−
<h5>Kloosterman su,m</h5>
+
<h5>Kloosterman sum</h5>
 +
 
 +
* Fourier coefficients
  
 
 
 
 

2010년 3월 5일 (금) 18:23 판

introduction
  • Hyperbolic distribution problems and half-integral weight Maass forms

 

 

Eisenstein series
  • z = x + iy in the upper half-plane
  • Re(s) > 1
  • definition
  • \(E(z,s) ={1\over 2}\sum_{(m,n)=1}{y^s\over|mz+n|^{2s}}\)

\(\DeltaE(z,s)=-y^2\left(\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}\right)E(z,s) = s(1-s)E(z,s)\)

 

 

Kloosterman sum
  • Fourier coefficients

 

 

history

 

 

related items

 

 

books

 

 

 

encyclopedia

 

 

question and answers(Math Overflow)

 

 

blogs

 

 

articles

 

 

experts on the field

 

 

TeX 
원본 주소 "https://wiki.mathnt.net/index.php?title=Maass_forms&oldid=42539"