"Maass forms"의 두 판 사이의 차이

2010년 3월 5일 (금) 18:45 판

z = x + iy in the upper half-plane
Re(s) > 1
definition
\(E(z,s) ={1\over 2}\sum_{(m,n)=1}{y^s\over|mz+n|^{2s}}\)
Maass form
\(\DeltaE(z,s)=-y^2\left(\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}\right)E(z,s) = s(1-s)E(z,s)\)
functional equation
\(E^{*}(z,s) = \pi^{-s}\Gamma(s)\zeta(2s)E(z,s) \)
\(E^{*}(z,s)=E^{*}(z,1-s)\)
a unique pole of residue 3/π at s = 1

@@ 62번째 줄: / 62번째 줄: @@
 * http://ko.wikipedia.org/wiki/
+* [http://en.wikipedia.org/wiki/Kronecker_limit_formula ]http://en.wikipedia.org/wiki/Kronecker_limit_formula
+* http://en.wikipedia.org/wiki/Real_analytic_Eisenstein_series
 * http://en.wikipedia.org/wiki/
 * http://en.wikipedia.org/wiki/
@@ 94번째 줄: / 96번째 줄: @@
 <h5>articles</h5>
-* http://en.wikipedia.org/wiki/Real_analytic_Eisenstein_series
 * [[2010년 books and articles|논문정리]]
 * http://www.ams.org/mathscinet